A woman's body was found on the vast estate in eastern England on New Year's Day, and Detective Chief Inspector Jes Fry said authorities are examining missing person reports and unsolved cases around the country to see if there are any links.
"We are at the very early stages of the investigation and it could be a complex inquiry," Fry said Tuesday. "The body had been there for some time."
Authorities were doing a post-mortem Tuesday on the body.
A member of the public found the body in a woodland at Anmer, a tiny village 115 miles (185 kilometers) northeast of London. The village is part of the Sandringham estate where the royal family spends some of its holidays.
The hamlet of Anmer is home to several dozen people and sits around three miles (4.8 kilometers) from Sandringham House, which has served as a private residence for British monarchs since 1862. Queen Elizabeth II and her husband Prince Philip spent part of the holiday season there and were at Sandringham House on New Year's Day.
Sandringham Estate's website says the entire estate is spread over 8,000 hectares (19,768 acres) in Norfolk. Sandringham House and its gardens make up 24 hectares (59 acres), and there are 240 hectares (590 acres) of woods and open countryside in a section that is open to the public free of charge all year.
There are also two stud farms and a fruit farm. The estate employs over 100 full-time staff.
Buckingham Palace referred all questions about the body's discovery back to police.