Detectives investigating Andrew Mountbatten-Windsor could investigate allegations of sexual misconduct as part of their inquiry into potential misconduct in public office.
Police have repeated their call for anyone with information to come forward.
It is understood police are concerned witnesses might think they are focusing on the narrow definition of misconduct in public office when it is a complex offence that can include abuse of position, sexual misconduct and corruption, among other things.
The police investigation into the former Prince Andrew was prompted by the release of US Department of Justice files related to its investigation into Jeffrey Epstein.
Mountbatten-Windsor has consistently and strenuously denied any wrongdoing, and has denied any personal gain from his role as a UK trade envoy between 2001 and 2011.
Epstein, who was convicted of soliciting prostitution from a minor in 2008, died in a New York prison in 2019 as he awaited trial on sex trafficking charges.
Mountbatten-Windsor was arrested on 19 February and released under investigation. He has only ever been described by Thames Valley Police as "a man in his 60s from Norfolk", as police forces do not usually name people unless they have been charged.
He was questioned on suspicion of misconduct in public office, after emails published in the Epstein Files seemed to suggest he had shared confidential information with Epstein.
His house on King Charles III's Sandringham Estate in Norfolk and his former home, Royal Lodge in Windsor, were both searched by detectives.
In a new update on the case, Thames Valley Police Assistant Chief Constable Oliver Wright repeated the force's call for information, saying: "We encourage anyone with information to get in touch with us."
"Misconduct in public office is a crime that can take different forms, making this a complex investigation," he said.
"There's a number of aspects of alleged misconduct that the investigation is examining."
It is understood police are concerned that witnesses and the public might think they are focusing only on the allegation that Mountbatten-Windsor shared a confidential trade reports with the late financier Epstein.
Misconduct in public office is a broad offence defined as someone who holds public office wilfully neglecting their duty by behaviour that can potentially encompass a wide range, also including things such as financial misconduct, abuse of position, and misconduct leading to personal gain.
It is understood detectives do not want people to think they are only focusing on potential misconduct involving "the state", rather than possible crimes that would involve people, which can also be part of a misconduct case.
So far Thames Valley Police have still not been formally given any information by the US Department of Justice related to the Epstein files and are relying on material released publicly.
In its update, the force said it had "been working with the United States Department of Justice to get further information that may be related to this investigation". The formal request for information is being channelled through the National Crime Agency.
It is understood detectives are happy with the co-operation they are getting from the UK government and the Royal Household.
There is ongoing liaison between police and the Crown Prosecution Service (CPS). Detectives are sharing information with lawyers at the CPS and getting "early investigative advice".
Thames Valley Police confirmed that they had already spoken to a number of witnesses.
The force is part of a national co-ordinating group of UK forces looking into information in the Epstein Files organised by the National Police Chiefs' Council.
This work includes contacting known victims of Epstein and encouraging others to come forward
"We hope that anyone with relevant information will come forward whenever they are ready to engage with us; our door is always open," Thames Valley Police said.
ACC Wright said: "There is a risk that the victim survivors may be put off from contacting us because they feel the weight of public, national and international focus will be too much for them."
If detectives were ever to think their investigation had encountered insurmountable problems they would have a duty to stop, but they have clearly not reached that stage.
But it is becoming obvious that there is little chance of the police and CPS being able to make a decision about whether to bring charges before 2027.
ACC Wright said "the investigation is continuing at pace".
Following a BBC report that a woman in her 20s was sent by Epstein to have a sexual encounter with Mountbatten-Windsor, police said in the update that they had been in touch with the woman's lawyer as part of their assessment of the allegation.
Thames Valley Police said: "We have engaged with the woman's legal representative to confirm that, should she wish to report this to police, it will be taken seriously and handled with care, sensitivity and respect for her privacy and her right for anonymity."
A formal investigation has not been opened.
