Preparations for possible action have been under way this week, according to Sky News' partner network NBC News.
The Pentagon has tailored options to meet the president's objectives, and they were due to be presented to him on Wednesday, two US officials and a person familiar with the discussions said.
The US has already begun withdrawing some military personnel from its Al Udeid Air Base in Qatar, the biggest American military base in the region. Sky News understands UK personnel were also leaving the same base.
Mr Trump declared earlier this week that "help is on its way" for Iranian protesters who have been met with a brutal crackdown from the regime, fuelling expectations of US military intervention.
A total of 2,615 people have been killed in the demonstrations, which began last month, according to the US-based Human Rights Activists News Agency, though other reports have suggested a much higher number.
Mr Trump also promised to take "very strong action" if the regime in Tehran goes ahead with executing protesters.
But speaking in the Oval Office on Wednesday, he claimed he'd been told the "killing in Iran is stopping".
A family member of one of those facing execution, Erfan Soltani, told Sky News there was no official announcement about his status on Wednesday.
But they added that Mr Soltani, 26, who was reportedly arrested last Thursday, could still face execution at any time.
Iran's foreign minister Abbas Araghchi claimed in a Fox News interview that no executions were planned.
'Any regime can fail'
In an interview with Reuters news agency, Mr Trump said he believed the protests could lead to the fall of the regime, which has been in place since the revolution of 1979.
"Any regime can fail," he said, adding: "Whether or not it falls or not, it's going to be an interesting period of time."
But he expressed doubt as to whether Iran's exiled crown prince, who has become a prominent voice spurring on protesters, could take over.
Mr Trump said Reza Pahlavi "seems very nice, but I don't know how he'd play within his own country".
Read more: Who is Crown Prince Reza Pahlavi?
Elsewhere, America's Western allies remain concerned about the situation across Iran.
The British embassy in Tehran has been temporarily closed, and the Foreign Office said it had "taken the precautionary measure to temporarily withdraw UK staff from Iran".
The UK already advises against all travel to the country.
Foreign ministers from the G7 group of nations, which includes the UK, also issued a joint statement on Wednesday to stress they were "gravely concerned by the developments surrounding the ongoing protests".
"The members of the G7 remain prepared to impose additional restrictive measures if Iran continues to crack down on protests and dissent in violation of international human rights obligations," the statement added.
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Meanwhile, Iran has now been cut off from nearly all telecommunications for more than six days, according to internet monitoring organisation NetBlocks.
The government began blocking internet access and international calls last Thursday as protests intensified.
Danish defence minister Troels Lund Poulsen said the joint operation would involve several allied countries, as he warned "no one can predict what will happen tomorrow".
Downing Street confirmed one UK military officer had been deployed at Denmark's request, while Germany, Sweden, Norway, and France will also be involved.
Denmark said the operation will "strengthen our ability to operate in the area", with Mr Trump having claimed only American control can protect the Arctic territory from Russia and China.
His vice president JD Vance and secretary of state Marco Rubio held talks with Danish officials at the White House on Wednesday, which Copenhagen said ended with "fundamental disagreement" about Greenland's future.
Danish foreign minister Lars Lokke Rasmussen said there was a "frank but also constructive discussion" during the meeting, but "our perspectives continue to differ".
"I must say the president has made his view clear, and we have a different position," he added. There was still a "fundamental disagreement" but both sides "agree to disagree".
The Danish foreign minister also announced a high-level working group will be set up "to explore if we can find a common way forward". The group is expected to meet for the first time "within a matter of weeks".
"The group, in our view, should focus on how to address the American security concerns, while at the same time respecting the red lines of the Kingdom of Denmark," he said.
Greenland's foreign minister Vivian Motzfeldt said the talks were held in a "respectful way" and added it is in their interests to "find the right path".
Trump: 'Unacceptable' if US doesn't control Greenland
The talks came after a Truth Social post from Mr Trump, who said it would be "unacceptable" if Greenland is not "in the hands of the United States".
He claimed the territory was "vital for the Golden Dome" - a giant, US version of Israel's missile defence system that experts have dismissed as physically implausible.
The US president also urged NATO to tell Denmark to keep China and Russia away from Greenland.
Leaders of the European Parliament "unequivocally" condemned Mr Trump's statements on Greenland and called on the EU Commission and Council to give concrete and tangible support to Greenland and Denmark.
"We respect the wishes of the Greenlanders and their interests, and they can count on us," EU Commission president Ursula von der Leyen said earlier on Wednesday.
Read more:
Trump on Greenland - 'one way or another'
Where could US strike next?
French President Emmanuel Macron echoed her remarks in a cabinet meeting, telling ministers if the sovereignty of a European country and ally was affected, the knock-on effects would be unprecedented.
"We do not underestimate statements on Greenland," Mr Macron said of US threats.
Danish defence minister Mr Poulsen confirmed Denmark and its allies would have a more permanent presence on Greenland going forward.
He described a US attack on the island as hypothetical, saying it was unlikely a NATO nation would attack another.
"We have implemented technological measures to prevent the Grok account from allowing the editing of images of real people in revealing clothing such as bikinis," said a statement.
"This restriction applies to all users, including paid subscribers."
It comes amid mounting condemnation in the UK and US of the chatbot's image editing capabilities, with British government ministers threatening the platform with action.
Sir Keir Starmer has described nonconsensual sex images produced by Grok as "disgusting" and "shameful", and media regulator Ofcom has launched an investigation.
The statement from X came hours after California announced its own state-level probe into the spread of sexualised images created by Grok, including of children.
Speaking at PMQs on Wednesday, Sir Keir had suggested action by the company may be imminent, telling MPs: "I have been informed this morning that X is acting to ensure full compliance with UK law.
"If so, that is welcome, but we're not going to back down, and they must act."
The controversy had seen X, which was bought by Mr Musk in 2022 when it was called Twitter, threatened with a potential fine or even ban in the UK.
Mr Musk, the billionaire owner of SpaceX and Tesla who has previously called for Sir Keir to be voted out of office, has claimed - along with Reform leader Nigel Farage - that a ban would be an attack on free speech.
Musk defends Grok safety measures
After the prime minister's comments at PMQs, Mr Musk wrote on X he was "not aware of any naked underage images generated by Grok".
"Obviously, Grok does not spontaneously generate images, it does so only according to user requests," he said.
"When asked to generate images, it will refuse to produce anything illegal, as the operating principle for Grok is to obey the laws of any given country or state.
"There may be times when adversarial hacking of Grok prompts does something unexpected. If that happens, we fix the bug immediately."
X had already announced in an earlier response to the political pressure that image creation and editing would be restricted to paid subscribers.
Technology Secretary Liz Kendall dismissed the move as merely "monetising abuse" and said the government would support Ofcom in whatever action it decides to take.
Ofcom's powers fall under the Online Safety Act, which states that online platforms have to make sure they're not hosting illegal content.
If X is found to not comply with the Online Safety Act, Ofcom can issue a fine of up to 10% of its worldwide revenue or £18m, and if that is not enough, can go as far as getting a court approval to block the site.
The Minnesota city has been a focus of the Trump administration's immigration crackdown, and tensions have flared since the fatal shooting of Renee Nicole Good.
She was shot in her car by an officer from ICE (Immigration and Customs Enforcement) on Wednesday 7 January.
The Trump administration claimed the shooting was an act of self-defence by the officer, declaring the woman used her vehicle as a weapon to attack him - a version of events rejected by state and local officials who say a bystander video showed her steering away.
The latest shooting came after hundreds more agents were deployed to the city.
It took place about 4.5 miles north of where Ms Good was killed.
According to the Department for Homeland Security, it happened shortly before 7pm local time on Wednesday after a targeted traffic stop of an illegal immigrant from Venezuela.
"In an attempt to evade arrest, the subject fled the scene in his vehicle and crashed into a parked car," it said in a statement. "The subject then fled on foot."
After catching up on foot, the officer was "violently" assaulted as the man resisted arrest.
As they struggled, two individuals allegedly emerged from a nearby home and attacked the officer with a snow shovel and broom handle.
The statement added: "As the officer was being ambushed and attacked by the two individuals, the original subject got loose and began striking the officer with a shovel or broom stick.
"Fearing for his life and safety, as he was being ambushed by three individuals, the officer fired defensive shots to defend his life. The initial subject was hit in the leg."
The officer and man who was shot are in hospital, while the other two people are in custody.
Protesters have since assembled near the scene of the shooting, and have been met by federal agents and police officers who fired tear gas into the crowd.
Read more from Sky News:
Iran's regime could fall, says Trump
X to block Grok from undressing images
'Organised brutality'
It came after a judge gave the Trump administration time to respond to a request to suspend its crackdown in the city, with assistant attorney general Brian Carter telling a court "the temperature needs to be lowered".
Governor Tim Walz has described what's happening in Minnesota as "a campaign of organised brutality", and said "accountability" would come through the courts.
The Department of Homeland Security says it has made more than 2,000 arrests in the state since early December.
The Pentagon is preparing to send military lawyers to Minneapolis to assist the government's case.
It's the first time in its 25-year history that a mission is being cut short due to such an incident.
NASA will not say which of the four astronauts is affected due to confidentiality, nor will it state what the problem is.
The person's condition is said to be stable and the space agency's medical chief, Dr. James Polk, said last week they were "erring on the side of caution".
The crew in the Dragon Endeavour spacecraft undocked just after 10.20pm UK time and drifted away from the space station.
Splashdown off California is being targeted for 8.41am on Thursday, according to an ISS post on X.
The crew is made up of Americans Mike Fincke and Zena Cardman, Russian Oleg Platonov and Japanese astronaut Kimiya Yui.
They arrived at the ISS via a Space X mission in August and were intending on staying for at least six months.
Sky News science correspondent Thomas Moore says up to now, ISS astronauts, backed by a flight surgeon and other medics on the ground, have been able to deal with all medical incidents.
These have included a blood clot in the jugular vein of an unnamed astronaut a few years ago.
The ISS has more than 190 drugs on board as well as medical equipment, including an ultra-sound machine, defibrillator and an intravenous therapy kit.
The emergency means the first planned spacewalk of 2026 has been cancelled. Cardman and Fincke were planning to venture outside to make preparations for some new solar panels.
"I'm proud of the swift effort across the agency thus far to ensure the safety of our astronauts," said NASA boss Jared Isaacman.
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The evacuation leaves three others behind at the ISS; NASA's Chris Williams and Russia's Sergei Mikaev and Sergei Kud-Sverchkov.
They arrived in November and are not due home until the summer.
NASA is planning on taking the 400-tonne space station - which circles the Earth at around 17,500mph - out of orbit in late 2030 or early 2031.
The structure will be brought down in the ocean, and the vision is for privately-funded space stations to fill the gap.