The allegation surfaced in a cache of legal papers unsealed by a USA judge in a defamation case involving a British socialite alleged to have supplied Jeffrey Epstein with underage girls.
A Buckingham Palace spokeswoman said: "This relates to proceedings in the United States, to which The Duke Of York is not a party".
The 59-year-old royal also shared the auto to Crathie Kirk on the Balmoral estate yesterday morning with his daughter, Princess Beatrice, while the Prince of Wales drove himself and the Duchess of Cornwall.
Ms Giuffre had also claimed she was forced into a sexual encounter with the Duke of York.
"And so then I sat on Andrew's lap, and I believe on my own volition, and they took the puppet's hands and put it on Virginia's breast, and so Andrew put his on mine". Prince Andrew is said that he had maintained a close relationship to the deceased billionaire.
Buckingham Palace has strenuously denied allegations by one of Epstein's former victims that she had sex with Andrew while under the age of consent.
After Epstein was arrested, Mr Trump told reporters he "knew (Epstein), like everybody in Palm Beach knew him", but added: "I had a falling out with him".
Epstein, 66, admitted prostituting minors in 2008 and spent 18 months in prison.
"I would not be surprised if a lot of British Royal names are being cited in this because it is well known that Mr Epstein and Prince Andrew were certainly socially acquainted".
His death has come under a cloud of intense scrutiny and is being investigated by the Federal Bureau of Investigation, given the number of high-profile figures he could have potentially incriminated following his arrest last month on charges of sex trafficking and conspiracy to engage in sex trafficking.
"I've known Jeff for 15 years", Trump said in 2002 NY magazine profile, going on to call him a "terrific guy".