Sir Mark told ABC News: “As we’ve said publicly with Peter Mandelson, the former ambassador, there is a particular e-mail to do with bailouts after the financial crash in the sort of, I think 2008-2009.
“It looks like it was shared with Epstein, so we’re looking at that as to whether that’s a criminal offence.”
He added that Thames Valley Police were also looking at other documents potentially shared by Andrew Mountbatten-Windsor.
The former prince is also under investigation on suspicion of misconduct in public office.
He was arrested after the force said it was assessing a complaint over the alleged sharing of confidential material with Epstein.
Sir Mark said there were also “a whole range of suggested sexual allegations” against Mountbatten-Windsor “and those are being assessed at the moment to see whether any of them do actually merit a criminal investigation”.