Detective Chief Inspector Jes Fry of the Norfolk Constabulary said officers were examining cold cases across the country for possible connections to the remains found on the queen's Sandringham Estate, the BBC reported Tuesday.
The estate is about 3 miles from the Sandringham House, where the queen is spending the holidays, on the 20,000-acre royal retreat.
"We are at the very early stages of the investigation and it could be a complex inquiry," Fry said. "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 BBC said forensic science experts were conducting a detailed search of the area.
Investigators said a dog walker made the discovery New Year's Day on the grounds of the estate, The Daily Telegraph reported.
"The remains were found by a member of the public who reported the incident to police on Sunday, Jan. 1, shortly after 4 p.m.," the Norfolk Constabulary said in a statement. "The area has been sealed off and a detailed search is currently being carried out."
A police spokesman said the queen and her husband were told of the find Monday.
In October, a tree surgeon discovered the body of a U.S. national, Robert James Moore, on an island in St. James Park near Buckingham Palace in London. Moore, who was apparently obsessed with the queen, set up a camp there and may have been dead for as long as three years.