Police Scotland is making inquiries into the activities of Andrew Mountbatten-Windsor, Jeffrey Epstein and Ghislane Maxwell during their time at Balmoral Castle.
The Daily Express reported that the inquiry relates to allegations that women were trafficked to the royal residence in Aberdeenshire.
Sex offender Epstein - who died in 2019 - and Maxwell, who was jailed in 2022 for sex trafficking , are understood to have visited the castle with Mountbatten-Windsor, who has previously denied any wrongdoing.
Police Scotland said inquiries were at "a very early stage" and that it would be inappropriate to comment further.
Representatives of Mountbatten-Windsor have been contacted for comment.
The Royal family traditionally spend summer at Balmoral, where Queen Elizabeth II died in 2022.
Asked about the Express report, a Police Scotland spokesperson said: "We have received information and active inquiries are ongoing but these are at a very early stage.
"All inquiries are evidence led, with the needs of victim survivors at the heart of those inquiries.
"We would never confirm details of ongoing enquiries and it would be inappropriate to comment further."
In February, the force said it wanted to "speak to anyone with information" about Epstein's private jet using Edinburgh Airport.
At the time officers said they had not received any reports or complaints in relating to the trip.
According to the Express, flight logs show Mountbatten-Windsor and Maxwell flew from Luton to Edinburgh on Epstein's private jet with two other passengers on 1 September 2006.
An image believed to show disgraced financier Epstein and former socialite Maxwell at Balmoral was also released by US prosecutors during her sex trafficking trial.
It is thought to have been taken in 1999, when Mountbatten-Windsor reportedly invited the couple to stay at the castle.
Epstein and Maxwell were reportedly regular guests at royal residences in the late 1990s and early 2000s.
Last year, the so-called Epstein Files were released by the US Department of Justice.
Among them was an email from someone named 'A' to Maxwell which said they were at Balmoral and asked for "new inappropriate friends".
The message, sent to Maxwell on 16 August 2001, begins: "I am up here at Balmoral Summer Camp for the Royal Family."
Later in the email, the sender asks: "How's LA? Have you found me some new inappropriate friends?" before signing off "see ya A xxx".
Jeffrey Epstein was 66 when he died by suicide in 2019 in a US prison while awaiting trial for sex trafficking charges.
Maxwell, 60, was jailed for 20 years in 2022 for her role in procuring girls for Epstein.
Last October it was confirmed Andrew had been stripped of his "prince" title and would be leaving his Windsor mansion, Royal Lodge.
In February he was arrested on suspicion of misconduct in public office , in the wake of information that emerged from the Epstein files in the US, and later released.
Earlier this month it emerged he was taking legal action against Thames Valley Police over search warrants issued before his arrest.
Mountbatten-Windsor has consistently denied any wrongdoing linked to his association with Epstein.
