Det Ch Insp Jes Fry, of Norfolk Constabulary, said officers were examining cold cases across the UK for potential links.
The force has confirmed the remains were that of a woman.
A dog walker made the discovery at Anmer, near King's Lynn, on New Year's Day. The area has been cordoned off.
Police said the identity of the woman was not yet known.
Detectives would not speculate on the age of the woman or comment on whether the body was clothed.
"We are at the very early stages of the investigation and it could be a complex inquiry," said Mr Fry.
"I cannot confirm whether she was clothed because, at the moment, only my staff, the person who found the body and the person or people who put it there know that - and I would like it to stay that way.
"The body has been in situ for some time but I can't comment on whether that is weeks, months or years.
"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 found in a wooded area on farmland at the 20,000-acre (8,000 hectare) royal estate.
Forensic science experts are carrying out a detailed search of the area - about a mile from the main gate to Sandringham House.
Mr Fry said it was not yet clear if the woman was killed at the scene or taken there after her death.
The body is expected to be recovered later and taken to the Queen Elizabeth Hospital, in King's Lynn, where post-mortem tests will take place.
The Queen and the Duke of Edinburgh, along with the Earl and Countess of Wessex, have been staying on the Sandringham Estate.
Buckingham Palace would not comment on the discovery, saying it was a "matter for Norfolk police".
A murder inquiry has begun after human remains were found on the Queen's Sandringham Estate in Norfolk.