When they were mixing with royalty, the US police had raided Epstein's Florida mansion and prepared an arrest warrant for him to answer child-sex allegations, the report added.
The photo was published in the Sun on Sunday, raising fresh questions about the prince's relations with the rich and powerful.
Andrew, 59, has said that he was not aware of the investigation or the warrant when he invited Epstein to Beatrice's party, adding that he had been invited as socialite Miss Maxwell's guest.
Weinstein's rape trial is set to start next month. The 67-year-old has denied the charges against him, including a sexual assault in 2006, the year he was caught on camera at Beatrice's party.
Maxwell has not been seen in public for several months and is under investigation by the FBI over claims that she procured girls for Epstein, who was found dead in prison earlier this year.
The Duke of York was forced to step back from his public duties last month after a disastrous television interview about his friendship with Epstein.
Several women want Andrew to be called as a witness over their claims that they were abused by Epstein. They say the duke saw young women giving massages at Epstein's homes in Florida and the Caribbean.