Mountbatten-Windsor, already cast out of the royal inner circle over his close relationship with Epstein, has faced fresh scrutiny since the recent publication of millions of new documents relating to the late convicted U.S. sex offender.
"The King has made clear, in words and through unprecedented actions, his profound concern at allegations which continue to come to light in respect of Mr Mountbatten-Windsor's conduct," a palace spokesperson said.
In the latest files released in the US, emails suggest he shared official United Kingdom trade documents with Epstein in 2010, after Epstein's conviction for child sex crimes, leaking information from his then-role as an official government envoy.
The documents appear to show that Andrew forwarded Epstein reports about Vietnam, Singapore and other places, which he had been sent in relation to an official trip.
Trade envoys are usually barred from sharing sensitive or commercial documents.
The 65-year-old second son of the late Queen Elizabeth has always denied any wrongdoing and has not responded to requests for comment since the latest release of Epstein files.
Thames Valley Police said the issue had been reported to them and that they were assessing whether to formally investigate.
The palace added: "While the specific claims in question are for Mr Mountbatten-Windsor to address, if we are approached by Thames Valley Police, we stand ready to support them as you would expect...
"As was previously stated, their majesties' thoughts and sympathies have been, and remain with, the victims of any and all forms of abuse."
The King's son Prince William and his wife Kate had said on Monday they were deeply concerned by the continuing Epstein revelations, in another pointed message from the royal family.
"Their thoughts remain focused on the victims," their spokesperson told reporters ahead of the prince's arrival on a high-profile trip to Saudi Arabia.
Mountbatten-Windsor was forced to quit all official royal duties in 2019 over his ties with Epstein and, in October, King Charles removed his title of prince.
Last week, he was forced to move out of his royal mansion.
In 2022, he settled a lawsuit brought by Virginia Giuffre which accused him of sexually abusing her when she was a teenager, through her association with Epstein.
Giuffre died in April by taking her own life.
While the royal family have attempted to distance themselves from Mountbatten-Windsor, he remains a thorn in their side.
"Charles, how long have you known about Andrew and Epstein?" a man shouted from the crowd as the King arrived in Clitheroe, northern England, the second time he had been heckled in a week.
Last week, police also said they were reviewing a new allegation against Andrew, triggered by the latest files, involving a woman being taken to an address in Windsor near London, where he has lived on the royal estate.
