Police announced the grim twist to the investigation after human remains were found on New Year's Day.
Detective Chief Inspector Jes Fry said cops are examining cold cases nationwide for potential links.
Mr Fry said: "We are at the very early stages of the investigation and it could be a complex inquiry.
"The body had been there for some time.
"The circumstances suggest this is a murder case and we are looking at missing persons reports and cold cases both locally and nationwide."
The body was spotted by a member of the public out walking, just hours after the royals attended their traditional church service.
Police immediately sealed off an area of woodland.
The estate, near King's Lynn, Norfolk, covers a massive 20,500 acres.
The Queen, 85, was seen riding her horse there only yesterday. She was still in residence last night with Prince Philip, 90, who is recovering from his heart op.
The royals spent Christmas at Sandringham.
Police last night said: "Detectives from Norfolk Constabulary have launched an investigation following the discovery of human remains in an area of woodland at Anmer, near King's Lynn.
"The remains were found by a member of the public who reported the incident to police on Sunday January 1 shortly after 4pm.
"The area has been sealed off and a detailed search is currently being carried out."
Buckingham Palace said it had no comment to make as it was "a matter for Norfolk police".