Labour's National Executive Committee (NEC) agreed to allow the mayor of Greater Manchester to contest the seat.
A Labour Party spokesperson said: "Labour's ruling body, the National Executive Committee has today given permission to Andy Burnham to stand in the candidate selection process in the forthcoming by-election for the Makerfield constituency."
Mr Burnham, who dodged questions when he was spotted jogging by Sky News on Friday, has already confirmed his intention to stand in the by-election after the current MP, Josh Simons, announced he would quit parliament to make way for Mr Burnham.
Mr Burnham said he has wanted to "bring the change we have brought to Greater Manchester to the whole of the UK and make politics work properly for people".
Starmer latest: Andy Burnham clears hurdle in by-election bid
Mr Burnham previously wanted to stand as the Labour candidate in the Gorton and Denton by-election but his bid was blocked by the NEC.
Applications for the candidate selection process close on Monday and the NEC will endorse a candidate on Thursday.
It is thought that the earliest date the by-election near Greater Manchester could take place is 18 June.
If he is successfully elected, Mr Burnham is widely expected to challenge Sir Keir for the party leadership.
Labour expects a stiff challenge from Reform UK in Makerfield, with Mr Simons securing a majority of just 5,399 over Nigel Farage's party at the 2024 general election.
Since then, Labour's polling collapse and Reform's surge have seen their positions reverse.
This month's May elections saw Reform win every council ward in the Makerfield constituency, securing around half the vote, while Labour won only a little more than a quarter.
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Allies of Wes Streeting have told Sky News' Ali Fortescue that he will stand in any future Labour leadership contest.
It followed his resignation as health secretary on Thursday, when he delivered an explosive letter to Sir Keir accusing his government of "drift" and the PM himself of leaving a leadership "vacuum".
However, he did not trigger an immediate leadership contest himself as expected, calling instead for a "broad" debate about the party's future.
He also said he backed Mr Burnham to be the candidate in the upcoming by-election.
In a post on X, the now-former health secretary wrote: "We need our best players on the pitch. There is no doubt that Andy Burnham is one of them.
"The Makerfield by-election will be tough. Votes will need to be earned. Andy is the best chance of winning and that should override factional advantage or propping up one person."
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Housing Secretary Steve Reed, a close ally of Sir Keir, has admitted the PM is "unpopular".
He told Sky News: "It's not a good week that we just had, let me put that on the table straight away.
"It reminds me of what went on under the Conservatives, and I think we need to draw that to a close as quickly as possible."
Asked if changing an unpopular leader was necessary to beat Reform UK at the next election, Reed replied: "The prime minister is unpopular, but each of the last four prime ministers, in turn, has been the most unpopular prime minister we've ever had."
Mr Trump told reporters on Air Force One en route to the US from China that Chinese President Xi Jinping had said releasing 78-year-old Mr Lai "would be a tough one".
The US president also told Fox News the response to him bringing up Mr Lai "was not positive".
"He went through a whole thing and I said, 'Well, we'd appreciate if you would release him. He's gotten old, and he's probably not feeling too well. It would be nice.' And I did not feel optimistic. I have to be honest with you about that one," Mr Trump told the broadcaster.
Mr Lai, the founder of the now-shuttered pro-democracy Apple Daily newspaper who was critical of Mr Xi and the ruling Communist Party, was sentenced to 20 years in jail in February under a national security law imposed by Beijing in 2020 that has virtually silenced dissent in Hong Kong.
Mr Lai's case sparked global concerns over the national security clampdown in Hong Kong, with observers saying his case symbolised a decline in freedoms that Beijing had promised when the former British colony returned to Chinese rule in 1997.
Foreign governments, including the UK and US, have raised concerns about Mr Lai - a British citizen - since he was arrested in 2020, but Hong Kong's government insists his case had nothing to do with press freedom.
Earlier this week, China's foreign ministry claimed Mr Lai had been a key planner of anti-China activities that aimed at destabilising Hong Kong. It added that the city's affairs are China's internal affairs.
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Meanwhile, Mr Trump told reporters he also talked to Mr Xi about potentially releasing Ezra Jin Mingri, a prominent pastor of an underground church who was arrested in China in November along with nearly 30 other pastors in what observers have called an escalating crackdown on religious freedom.
"He said he's gonna strongly consider the pastor," Mr Trump said.
Mr Jin and the other pastors of the underground Zion Church were arrested after new rules from China's top religion regulator banned unauthorised online preaching or religious training by clergy, as well as "foreign collusion".
The families of both Mr Jin and Mr Lai said they appreciated Mr Trump for raising their cases with Mr Xi.
Mr Jin's daughter, Grace Jin Drexel, said her family and supporters were "overjoyed" to hear what Mr Trump had said about her father, calling it "nothing short of miraculous".
"We could not be more grateful to President Trump and his skillful administration for pressing the case," she said.
Despite Mr Trump's far less optimistic tone on Mr Lai, the former media mogul's daughter, Claire Lai, said she also was grateful to the US president and his administration for the commitment shown to her father's release.
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"He has earned his reputation as liberating the unjustly detained and I am confident he and his administration will be the ones to free my father," she said.
She said this was an opportunity for Mr Xi to do "the only just and honourable thing" for Mr Lai and to show a gesture of goodwill to the world by releasing a man she said had dedicated himself to Hong Kong.
Armoured vehicles, police horses, dogs, drones and helicopters, along with 4,000 officers, will be deployed as the Metropolitan Police hopes to avoid clashes between Tommy Robinson's Unite the Kingdom march and the pro-Palestine Nakba Day rally.
Also today, Chelsea and Manchester City are due to clash in the FA Cup final, leaving police concerned that some football fans could go straight from the game to the rallies.
Prime Minister Sir Keir Starmer said ahead of the Unite the Kingdom march: "We're in a fight for the soul of this country, and the Unite the Kingdom march this weekend is a stark reminder of exactly what we are up against. Its organisers are peddling hatred and division, plain and simple."
The Met has confirmed they will arrest individuals who incite hatred, and new guidance urges prosecutors to consider whether protest placards, banners and chants viewed on social media may amount to offences of stirring up hatred during the rallies.
For the first time under official protest restrictions, organisers and speakers both face prosecution if their rally is used as a platform for extremism or hate speech.
In another first for a policing operation around a protest, live facial recognition will be used, with cameras set up in a location in Camden, north London.
Deputy Assistant Commissioner James Harman said the "unprecedented" operation will cost the force £4.5m, with £1.7m being spent to bring in officers from other forces to boost numbers.
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He said today "has the potential to be one of the busiest days for policing in London in recent years".
Some 50,000 people will attend the Unite the Kingdom rally, with 30,000 more at Nakba Day, police estimate.
The government has blocked 11 foreign nationals described by Sir Keir as "far-right agitators" from entering the UK ahead of the Unite the Kingdom rally, including US-based anti-Islam influencer Valentina Gomez.
Italy's foreign ministry said the group had been exploring underwater caves in the Vaavu Atoll at a depth of around 50 metres (165ft) on Thursday.
It gave no further details about the victims' identities or the cause of the accident, but said all five were Italian nationals and an investigation was under way.
The University of Genoa named four of the victims as professor of ecology Monica Montefalcone, her daughter Giorgia Sommacal, who was a student, research fellow Muriel Oddenino, and marine biology graduate Federico Gualtieri.
In a statement posted on its website, the university said: "The sympathy of the entire university community goes out to the families, colleagues and students who shared their human and professional journey."
The fifth victim was named in Italian media reports as boat operations manager and diving instructor Gianluca Benedetti.
Ms Montefalcone's husband, Carlo Sommacal, told Italian outlet La Repubblica that his wife was an "expert" and had done 5,000 dives. "She knows what to do even in times of difficulty," he added.
Mr Sommacal said the same goes for Mr Benedetti, who he described as "meticulous" and said: "He checked everything: the tanks, the weather conditions. He's not a fool."
He said he hopes his wife and daughter's bodies are found for his and his son Matteo's sake, but also because "Monica usually had a GoPro when she went diving".
"I don't know if she had one the other day. If they find it, maybe from there we can understand what happened," he said.
Ms Montefalcone was an award-winning marine biologist, well known for her TV appearances and commitment to conservation projects, and was previously interviewed on Sky TG24.
"I have dedicated my entire life to discovering and studying the wonders that live beneath the surface of our seas," she told a local TV station, according to Sky TG24, after receiving the 2022 Atlantide Prize for her contribution to the understanding of marine ecosystems and her commitment to marine conservation.
The divers were reported missing at around 1.45pm by the crew of a diving vessel they were travelling on, when the group failed to resurface.
Conditions were described as unfavourable at the time, with a yellow weather alert in effect.
A large-scale search and rescue operation was launched by the Maldivian Coast Guard and the Maldives National Defense Force (MNDF). Boats, aircraft and dive teams were deployed to the area.
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"A body has been found among the five divers who dived in Vaavu Atoll," the MNDF said in a statement to Italian news agency ANSA.
"The body was found inside a cave. The other four divers are believed to be inside the same cave, which extends to a depth of approximately 60m."
Search teams were preparing for a second dive on Friday to locate the remaining four divers.
Italy's foreign ministry added that the Italian embassy in Sri Lanka was working to contact the victims' families and provide consular assistance.
Even when liquidated Rangers had to start again in the fourth division in 2012, Celtic was still always ending the season at the summit without a serious challenger.
Jeopardy had to be found elsewhere in the Premiership or down the leagues.
Not, finally, this most captivating of seasons. One group of players has led the way since September, but they are the gatecrashers from Edinburgh.
Whether Heart of Midlothian could hold on to the lead has been gripping for the game, agonising for Derek McInnes' side.
But they could leave Celtic Park this afternoon having broken up the duopoly.
The hope will be for a day about football, without rancour between fans or threats to referees.
With Hearts holding a one-point advantage, just avoiding defeat to Celtic will seal their first title since 1960, in a finale for the ages.
It has been so long since the trophy last ended the season outside Glasgow that the win was masterminded by pre-Manchester United Alex Ferguson with Aberdeen in 1985.
Hearts will not want a reminder of the following season, the last time they came within touching distance of glory, only to lose out to Celtic on the final day.
No wonder so many scoffed at betting tycoon Tony Bloom's claim last June on buying into Hearts that he could disrupt the dominance.
Not even he imagined it could happen this quickly, evoking memories of Leicester's 5,000-1 Premier League title upset a decade ago.
And it's happened without outspending Celtic and Rangers, albeit benefiting from an unusual season of simultaneous struggles for both of the Old Firm.
There has not even been enough time for Mr Bloom to fully implement the analytical expertise that has served Brighton so well in the Premier League.
Separated by a border, the financial disparities between the Premier League and Scottish Premiership are stark.
While buying 29% of Hearts cost Mr Bloom £9.86m, Brighton would be worth hundreds of millions. And while Brighton generated £222m last season, Hearts banked just £24.4m.
That Celtic were making almost £144m at the same time highlights the gulf within Scottish football, too.
There are Celtic and Rangers with 55 championships apiece, followed in the roll of honour by Hearts, Aberdeen and Hibernian in joint third with only four titles each.
So today is about providing hope to fans - just as Leicester did - that one day it might finally come good for your team and you'll be the ones with the parade.
Fans will also reflect on the journey and the torment.
The chance to be crowned champions of Scotland would have seemed unimaginable 12 years ago when just surviving as a club was the priority.
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"Can we keep ripping the script up?" Mr McInnes wondered on the eve of the trip to Celtic. "We have ripped the script up this season and I think from the first game of the season, nobody would have anticipated that we could be in this position."
It's why Hearts go to Celtic bullish, with belief this will be their day, their time to show you do not have to be weighed down by the baggage of expectation that a Scottish season begins with one question: will it be the year of Celtic or Rangers?
This has been Heart of Midlothian's year, even before any silverware is handed out.