But Virginia, who is now married and has the surname Giuffre, tells the show: 'It was a really scary time in my life.
"[The prince] knows what happened, I know what happened".
Prince Andrew, the Duke of York, has in recent months been in the spotlight for his increasingly scandalous relationship with the dead sex offender Epstein.
Sources told Britain's The Sun that there is talk behind closed doors that the Queen, who has cut down on her royal duties and appearances in recent years, can not continue forever and that she will "retire" in April 2021 when she turns 95.
The woman, Virginia Roberts Giuffre, has said she was trafficked by Epstein and had sex three times with Prince Andrew starting in 2001, including once in London.
The fallout has been made abundantly clear this week with the absence of Andrew's name on the list for the North Atlantic Treaty Organisation leaders reception at Buckingham Palace.
Roberts, now known as Virginia Giuffre, made the comment in a BBC interview that is scheduled to air on Monday.
The London police, he added, would not be the "appropriate authority" to investigate.
One Inverness resident, who did not want to be identified, said: "The Highland Hospice has - quite rightly - chosen to disassociate itself from Prince Andrew and have removed the plaque commemorating the opening which he attended".
As the story dominated British news for a week, overshadowing campaigning for the December 12 election, there has been widespread criticism of Andrew and demands he should answer questions from US authorities about Epstein.
Earlier on Thursday, the Metropolitan Police defended its decision not to investigate a claim of trafficking by Ms Giuffre.
The allegation related to trafficking to central London in March 2001.
"The MPS always takes any allegations concerning sexual exploitation seriously".
The interview has been widely considered a public relations disaster for Andrew, who announced shortly after it aired that he would be stepping down from his royal duties.
"Following the legal advice, it was clear that any investigation into human trafficking would be largely focused on activities and relationships outside the UK".
Epstein was being held on sex trafficking charges at a federal prison in Manhattan when he killed himself August 9. The alleged incident which is said to have occurred on June 30, 2000, was a security breach as the woman was not searched and did not sign in when entering the royal palace.