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.
Asked about the latest reports, Scottish First Minister John Swinney said: “I understand the seriousness of the points that have been made and the concern that has been expressed.
“This is an operational matter for Police Scotland to fully and comprehensively investigate and I’m very confident that’s exactly what Police Scotland will do.”
Prime Minister Andy Burnham said he did not want to comment on the police inquiries, which “should properly be independent”.