Separately, Thames Valley Police is also assessing whether there are grounds to investigate Andrew for suspected misconduct in public office and breach of official secrets.
Asked whether he thought Andrew should voluntarily speak to UK police, Sir Keir said: “I think that’s a matter for the police.
“They will conduct their own investigations, but one of the core principles in our system is that everybody is equal under the law and nobody is above the law.”
He added: “It’s a very important principle of our country… and it has to apply in this case in the same way it would in any other case.”
The prime minister said that, if MPs in Parliament wanted a debate on Andrew’s links to Epstein, he “wouldn’t stand in the way”.
Thames Valley Police is currently assessing allegations, first reported by the BBC, that a second woman was sent to the UK by Epstein for a sexual encounter with Andrew.
The encounter allegedly occurred at the former prince’s residence, Royal Lodge, in 2010. The woman, who is not British, was in her 20s at the time.
The woman’s lawyer, Brad Edwards, said that after spending the night with Andrew, the woman alleges she was given tea and a tour of Buckingham Palace.
Millions of files released last month by the US Department of Justice shed new light on Andrew’s close relationship with the disgraced financier.
The latest tranche included pictures of him kneeling on all fours over a woman lying on the ground, while other files repeatedly reference him.
They also show the former prince forwarded sensitive government documents and commercial information to Epstein.
In his interview with Breakfast on Thursday morning, Sir Keir reiterated previous comments he made suggesting Andrew should testify before the US Congress.
“Anybody who has any information should testify. So, whether it’s Andrew or anybody else, anybody whose got relevant information should come forward to whatever the relevant body is,” he said.