Andrew told BBC Newsnight he first met the since-disgraced financier through "his girlfriend back in 1999".
U.S. officials are investigating claims that Epstein, who was found dead in prison previous year, trafficked women and girls around the world to be abused.
Andrew's help is being sought as a witness, his lawyers said.
Ghislaine Maxwell allegedly acted as Epstein's "madame" and a "primary co-conspirator" to his crimes. Virginia Roberts Giuffre claims Epstein forced her to have sex with Andrew in 2001.
Epstein is released from jail.
What could happen next with Prince Andrew?
Allegations against Jeffrey Epstein started surfacing in 2005 when the parents of a 14-year-old girl told police in Florida that Epstein had molested their daughter at his Palm Beach home.
Rather than draw a line under allegations, it raised more questions than answers, particularly given Prince Andrew's freakish claims that he didn't sweat and had a Pizza Express alibi.
The woman, Virginia Giuffre, alleges she was trafficked under-age to have sex with friends of Epstein, who was 66 when he killed himself in a NY jail in August previous year.
The Duke of York has been accused of attempting to "falsely portray himself to the public as eager and willing to co-operate" with USA authorities investigating convicted sex offender Jeffrey Epstein.
Presenter Emily Maitlis wrote on Twitter that it was a "no questions vetted" exchange. His cousin Lady Butter (a great friend ever since his regular long stays with her family at Luton Hoo in the 1930s) commented this week: "The secret is that he still does everything he has previously done, but slower".
Two months later, Prince Harry, Philip's grandson, and his wife, the former Meghan Markle, caused further controversy when they announced they were stepping away from royal duties so they could seek financial independence in North America.
MLA requests are "methods of cooperation between states for obtaining assistance in the investigation or prosecution of criminal offences". These statements were inaccurate, and they should not have been made.
It comes after businesses, charities and universities begin to cut ties with the duke following the "car crash" interview.
In early March, Mr Berman also claimed the Prince had "shut the door" on USA authorities. Currently, he is the subject of an expansive documentary series on Netflix titled: Jeffrey Epstein: Filthy Rich.
The Duke categorically denies he had any form of sexual contact or relationship with Giuffre.
Andrew's legal team has insisted the royal has made three offers to help with the probe into his former associate but the US Attorney for the Southern District of NY said a request to schedule an interview has been repeatedly declined.
Prince Andrew's lawyers say he has offered his testimony at least three times, and that the USA prosecutors are giving an "entirely misleading account" in claiming he hasn't offered cooperation.
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