Mountbatten-Windsor and Mandelson were separately arrested in February following the release of millions of documents by the US Department of Justice relating to the late sex offender Jeffrey Epstein.
Neither have been charged with any criminal offence and both men have denied any wrongdoing, saying they regretted their association with Epstein.
Mountbatten-Windsor was arrested on suspicion of misconduct in public office, relating to the possible sharing of sensitive information with Epstein when he was special representative for trade and investment between 2001 and 2011.
Police investigating Mountbatten-Windsor have also said they are assessing reports that a woman was taken to an address in Windsor in 2010 for sexual purposes.
Mandelson, meanwhile, is under investigation following claims he leaked market-sensitive information to Epstein while a government minister during the financial crash.
But the United Kingdom's Director of Public Prosecutions Stephen Parkinson told reporters in relation to Mandelson: "It is a case of some complexity and it would be wrong to focus on a single event or a single transaction."
He said: "I really don't think that anyone should expect an early resolution of the investigation.
"It would not be at all surprising if it took over a year, not because of any lack of urgency but because of the complexity and also the international dimension."
Parkinson added that the same issues and likely timescale also applied to the investigation into Mountbatten-Windsor.
