The force said it was made aware of two people attempting to enter the base - where submarines that carry the UK's Trident nuclear deterrent are based - at around 5pm on Thursday.
A spokesperson said: "A 34-year-old man and 31-year-old woman have been arrested in connection and enquiries are ongoing."
According to the PA news agency, the man arrested is Iranian.
A Royal Navy spokesperson said: "Police Scotland have arrested two people who unsuccessfully attempted to enter HM Naval Base Clyde on Thursday 19 March.
"As the matter is subject to an ongoing investigation, we will not comment further."
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Sky's defence and security analyst Michael Clarke noted that the site in Faslane is "the biggest military base in Scotland", with around 6,000 to 7,000 people there, "both civilians and military".
"Faslane is probably Britain's most important single installation", he added. "We have seven attack submarines. And if they're all out of maintenance, then this is where they operate from."
The inquest in Stockport was told that the former world champion was more than twice the alcohol drink drive limit at the time of his death.
Alison Mutch, senior coroner for South Manchester recorded hanging as the cause of death but did not record a conclusion of suicide.
The coroner said that while he was the person who caused his own death, it was not clear that the 46 year-old intended to take his life.
She said police found no notes or anything that gave any suggestion of an intent to take his life.
He had been under the influence of alcohol and there were also brain changes identified by the pathologist at his post mortem as chronic traumatic encephalopathy (CTE) - a brain disease caused by repeated head trauma in contact sports like boxing.
The condition can cause mood swings, confusion and forgetfulness, things his family said they had noticed.
The coroner said it was not possible to determine how much of an impact this had had on his death, so she recorded a narrative verdict.
The inquest opened with some statements from several of Hatton's family members who painted a picture of a man who was deeply loved and appreciated by them - and for whom his death came as a shock.
His son Campbell said he was "fearless" inside the ring, but had struggled outside, having been open about his issues with mental health, drugs and alcohol.
But said before his death his father "was in the best place he'd been in years".
His former partner Jennifer, the mother of his two daughters, echoed this. She called him an "active present and loving father - seeing the girls multiple times a week".
And she said when they went for dinner as a family on 12 September - the last time anyone saw him alive - he was making positive and detailed plans with the girls. He wanted the whole family to come and watch his upcoming fight in Dubai
The dinner was "fun" and he seemed "completely normal". After dropping his family off he told them he would see them in a couple of days.
DS Helen Grigolis from Greater Manchester Police then described the hours leading up to the boxer's death.
She said Ricky Hatton had not come out to meet his driver for an event as expected on 13 September.
His manager, Paul Speak, then arrived at his house around 6.30 in the morning the next day to pick him up for a flight to Dubai.
He tried calling him and opened the gate, and eventually used his own key.
He heard music coming from the games room - went in and found Mr Hatton already dead.
A post mortem had found evidence of alcohol being consumed in the hours before his death - when he died he was well over twice the drink drive limit - and of previous cocaine and cannabis use, but not as recently.
The inquest heard the pathologist had examined a brain sample and found changes unusual for someone his age - mostly commonly found in older adults with Alzheimers.
In 2023, the boxer spoke about his personal life and continuing mental health battles in a Sky documentary.
Hatton was the most popular British fighter of his era and tens of thousands of fans followed him to Las Vegas for his biggest fights.
"The Hitman" won the world title with a stunning win over favourite Kostya Tszyu in 2005 and went on to fight all-time greats such as Floyd Mayweather and Manny Pacquiao - ultimately losing.
In July, he announced he was coming out of retirement for a December bout in Dubai, 13 years on from his last pro fight. Hatton was meant to be flying there on the day he was found.
Thousands turned out on the streets of Greater Manchester for Hatton's funeral procession in October to pay their respects. The likes of Liam Gallagher, Andrew Flintoff, Wayne Rooney and Tyson Fury also attended.
His son, Campbell, 24, told the service: "I can't explain how much I'm going to miss you dad, and that we won't be making any new memories - but the ones we did I will cherish forever."
His daughters, Fearne, 12, and Millie, 13, also gave emotional tributes.
Anyone feeling emotionally distressed or suicidal can call Samaritans for help on 116 123 or email jo@samaritans.org in the UK. In the US, call the Samaritans branch in your area or 1 (800) 273-TALK.
James Bubb, who now identifies as a woman named Gwyn Samuels, assaulted the victim multiple times when she was between the ages of 12 and 18.
Samuels was sentenced to a total of 32 years, made up of 24 years' imprisonment and a further eight years on extended licence, at Aylesbury Crown Court on Friday.
The ex-Metropolitan Police volunteer sexually assaulted the child in public shortly before her 13th birthday.
A jury found Samuels guilty of one count of raping a child under 13, one count of sexual activity with a child, one count of assault of a child under 13 by penetration, and one count of assault by penetration.
She was found not guilty of one count of rape and one count of sexual activity with a child in relation to that complainant, but was also found guilty of one count of rape against a second person.
In sentencing, Judge Jonathan Cooper said Samuels "abused the most intimate trust of your victims" in "a campaign of abuse against each that was intended to break their will entirely".
Samuels, who identified as a male at the time of the offences, made contact with both victims online, the first in 2018, when the former police volunteer was around 21 and she was 12 years old.
They then met in person for the first time at a Christian festival a few months later, the court was told.
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The second complainant was a woman Samuels met online while posing as a 16-year-old girl.
They met when the woman had just turned 18, and were in an on-off relationship between January 2018 and February 2023.
Samuels started training with the Met in 2020. The first victim said the defendant spoke "a lot about the powers he had" in their role as a special constable.
The second complainant said Samuels used "BDSM and kink as a way of creating control" over her, and that he would "use police training techniques" on her.
"The control, the power he got, it sure as hell wasn't consensual," she told police.
The judge said he understood the defendant, who has been in the male prison estate while in custody, will stay there.
"The key point is that you are a very significant risk to women," Judge Cooper said.
"This is not predicated on your trans status, but on your criminal status."
Large parts of the southwest of the United States are trapped in a dangerous heatwave, made worse in some places by a heat dome, with temperatures reaching around 43C (110F) at testing sites.
The heatwave has shattered March temperature records all over the southwest of the country, with hot weather arriving months ahead of schedule.
"This is what climate change looks like in real time: extremes pushing beyond the bounds we once thought possible," said University of Victoria climate scientist Andrew Weaver.
March's heat would have been virtually impossible without human-caused climate change, according to a report released today by World Weather Attribution, an international group of scientists who study the causes of extreme weather events.
The area of the US being hit by extreme weather in the past five years has doubled compared with 20 years ago, according to the National Oceanic and Atmospheric Administration's Climate Extremes Index.
The extreme conditions are expected to persist and expand east in the coming days.
Across Southern California and the Desert Southwest, around 38 million people are under heat alerts.
Phoenix recorded its earliest triple-digit day on Wednesday, with a high of 38.8C (102F).
Temperatures in the city reached 40C (104F) on Thursday.
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"This is not only the first 100F (37.8C) day of 2026, but it is also the earliest occurrence of 100° in Phoenix (which last occurred on 26 March 1988)," the local office of the National Weather Service wrote on X.
Phoenix is forecast to hit 41C on Friday and Saturday, with an extreme heat warning in effect for the region.
Las Vegas in neighbouring Nevada also saw a new March record, with temperatures reaching 35C.
Temperatures could reach 37.7C there today.
Records could also be set in Colorado, as this week's heat dome continues to trap hot air over the southwest of the country.
The release of files related to the late sex offender has sent shockwaves around the world, revealing his ties to prominent people, including Crown Princess Mette-Marit.
They showed frequent communication between her and the disgraced financier long after he pleaded guilty in 2008 to soliciting an underage girl.
Simply being named in these files does not suggest any wrongdoing, and the crown princess has not been accused of any criminality.
While her ties to Epstein were already reported, new documents showed a more extensive relationship.
The revelations prompted a rare rebuke from Norwegian Prime Minister, Jonas Gahr Stoere, who said it was important that she answer questions about her relationship with Epstein.
Speaking with NRK, the country's public broadcaster, an emotional Mette-Marit said: "I was manipulated and deceived."
"Of course, I wish I had never met him," she added.
The files revealed the crown princess maintained contact with Epstein from 2011 to 2014.
They also show she stayed at his Palm Beach house for four days during a private trip in 2013.
"He used the fact that we had a mutual friend, and that I'm gullible," she said.
"I like to believe the best about people. But I also chose to end contact with him."
"I've never seen anything illegal," she told NRK.
The files also appeared to contradict her 2019 statement when she apologised for not investigating Epstein's past, and said she would never have associated with him had she known the seriousness of his crimes.
In one email from October 2011 - three years after Epstein's guilty plea - she told the disgraced financier she had Googled him.
"It didn't look too good" she wrote, followed by a smiley face.
She told NRK she could not remember why she wrote the email.
"But if I had found information that made me realise that he was an abuser and sex offender, I wouldn't have written a smiley face behind it," she continued.
Mette-Marit is married to Crown Prince Haakon, the heir to the throne, who sat beside his wife, and said he supported her at a difficult time.
He said marriage was for "the good days and the bad", praised her as "caring, wise and really strong", and insisted he will "always have her on the team".
The crown princess suffers from a chronic lung disease that will eventually require her to have a lung transplant, and she has not appeared in public in recent weeks.
Her interview comes after Marius Borg Hoiby, her eldest son from a previous relationship, went on trial accused of rape and other crimes.
The 29-year-old has pleaded not guilty to rape and domestic abuse while admitting some lesser charges.
The popularity of Norway's royal family has taken a hit in recent months, with a February survey showing some 60% of Norwegians supported the monarchy, down from 70% in January.