The investigation centers on the time Mountbatten-Windsor spent with the convicted sex offender, who visited Balmoral in 1999, reportedly on the invitation of the then Prince Andrew. An undated photo from US Department of Justice files appears to show Epstein and Maxwell at a log cabin on the estate.
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 inquiries and it would be inappropriate to comment further."
The Daily Express reported that the inquiries relate to claims that women were trafficked to the estate in the Scottish Highlands.
This is the latest in a series of investigations into Mountbatten-Windsor's ties to Epstein. In February, Thames Valley Police arrested the former duke on suspicion of misconduct in public office. He was released under investigation. Several forces, including Thames Valley Police, the Metropolitan Police and Surrey Police, also have live investigations linked to the release of the Epstein files, the National Police Chiefs' Council said.
An NPCC spokesperson said that identifying further potential offending, suspects, victims or witnesses is a complex process that will take time, but UK policing is committed to assessing the material released by the US Department of Justice. The NPCC said there is no national investigation at present.
King Charles stripped his brother of the title Duke of York late last year and removed other honours. Mountbatten-Windsor has consistently denied any wrongdoing over his links to Epstein.
Emails released as part of the Epstein files have raised further questions. An email signed "A" asked Maxwell for "inappropriate friends".
Mountbatten-Windsor served as the UK's special representative for international trade and investment from 2001 to 2011, stepping down as scrutiny of his friendship with Epstein grew.