But the prince claims he did not witness or suspect any suspicious behaviour during his visits to Epstein’s homes.
Mr Boies said: “One of the things that we have tried is to interview Prince Andrew and to try to get what his explanation is.
“He was a frequent visitor. They ought to submit to an interview. They ought to talk about it.”
The subpoenas are said to have been prepared for all five cases and would need to be signed off by a judge once the prince was on US soil.
Prince Andrew would then be able to challenge the subpoena in court if he did not want to give evidence.
The Duke of York is facing fresh scrutiny over allegations he had sex with a trafficked teenager and about his association with convicted sex offender Jeffrey Epstein.
Andrew’s accuser Virginia Giuffre called on the British public to stand up beside her in her fight as she told BBC Panorama how the duke was “the most hideous dancer I’ve ever seen in my life” and “his sweat was ... raining basically everywhere”.
“I was just like grossed out from it, but I knew I had to keep him happy because that’s what Jeffrey and Ghislaine [Maxwell, his then-associate] would have expected from me,” she said in her first UK television interview.
Ms Guiffre claims she was trafficked by the since disgraced financier Epstein and forced to have sex with Andrew when she was a teenager, which the duke categorically denies.
The Panorama investigation broadcast on BBC One on Monday night disclosed that five women who allege they were victims of paedophile Epstein are calling on Andrew to give a testimony in their civil court case.
They claim the duke saw people being given massages at Epstein’s homes.
The Queen’s second son, who stepped down from public duties just over a week ago, insisted in his disastrous Newsnight interview that he did not witness or suspect any suspicious behaviour during his visits to Epstein’s homes in Florida, New York and the Caribbean.
Panorama claimed it had also uncovered an email allegedly sent by Andrew in 2015 to Ms Maxwell, who is accused of procuring girls for Epstein.
In it, the duke is alleged to have asked for Ms Maxwell’s help in dealing with claims by Ms Guiffre, who was previously known as Virginia Roberts.
The programme claimed the message was sent at 5.50am on 3 January, 2015, after Ms Giuffre lodged court papers in the US.
Andrew’s attempts to defend himself against Ms Giuffre’s previous accusations and explain his friendship with Epstein in a BBC Newsnight interview last month were branded a “car crash” and led to him withdrawing from public duties.
A Buckingham Palace spokesman said in response to the allegations on Panorama: “It is emphatically denied that The Duke of York had any form of sexual contact or relationship with Virginia Roberts. Any claim to the contrary is false and without foundation.”
On the duke’s association with Epstein, the palace spokesman added: “The Duke of York unequivocally regrets his ill-judged association with Jeffrey Epstein. Epstein’s suicide left many unanswered questions, particularly for his victims.
“The Duke deeply sympathises with those affected who want some form of closure. It is his hope that, in time, they will be able to rebuild their lives.
“The Duke is willing to help any appropriate law enforcement agency with their investigations, if required.
“The Duke has already stated that he did not see, witness or suspect any behaviour of the sort that subsequently led to Jeffrey Epstein’s arrest and conviction.
“He deplores the exploitation of any human being and would not condone, participate in, or encourage any such behaviour.”
Ms Giuffre claimed in court papers in Florida that she was forced to have sex with Andrew when she was aged 17, below the state’s age of consent.
She alleges the duke slept with her on three separate occasions, twice while she was underage.
During his Newsnight interview, the duke said an alleged encounter with Ms Giuffre in 2001 did not happen as he spent the day with his daughter, Princess Beatrice, taking her to Pizza Express in Woking for a party.
Epstein was found dead in his New York prison cell in August, where he was being held on sex trafficking charges.
Ms Giuffre’s interview took place before the duke’s appearance on Newsnight.
Additional reporting by agencies