Police are reportedly investigating whether Andrew Mountbatten-Windsor behaved inappropriately towards a woman at Royal Ascot.
The alleged incident occurred in 2002 when the late Queen Elizabeth II attended the annual horse race in Berkshire with other senior royals.
The Sunday Times said it is unclear whether the claim was reported to police at the time or more recently.
Thames Valley Police told Metro: ‘We cannot go into specifics of the investigation, but we are following all reasonable lines of enquiry.’
The force, which covers Windsor and Ascot in Berkshire, is still investigating Andrew for potential misconduct in public office.
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He was arrested on his birthday in February on suspicion of sharing confidential information with the convicted late sex offender Epstein during his time as the UK trade envoy.
Police officials said on Friday that they are considering widening their investigation to include claims of sexual misconduct against Andrew.
A woman claims she was sent by Epstein to the Royal Lodge to have sex with Andrew in 2010, followed by a tour of Buckingham Palace.
She was in her 20s when the alleged incident is said to have taken place, her lawyer, Brad Edwards, told the BBC.
Andrew has denied wrongdoing over his links to Epstein.
Detectives expect their investigation to be lengthy, given the complicated nature of the inquiry.
They are now considering material recovered during searches at the ex-prince’s home on the Sandringham Estate and at Windsor’s Royal Lodge.
A formal request has also been made to the US Department of Justice to obtain the original versions of the Epstein files.
Thames Valley Police Assistant Chief Constable Oliver Wright said: ‘We encourage anyone with information to get in touch with us through the normal non-urgent contact channels, such as the Thames Valley Police online portal.’
The former prince served as the UK’s special representative for international trade and investment from 2001 until 2011.
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