It's thought the Duke and Duchess of Cambridge - seen here on their visit to the city they're named after in November - will be given Anmer Hall on the Sandringham estate.
The couple are expecting their first baby later this year.
The late Georgian country house is just two miles east of the Queen's Sandringham House and was once home to the Duke and Duchess of Kent. It's currently leased out to a tenant.
The 20,000-acre Sandringham estate near King's Lynn in Norfolk has been owned by the Queen since her accession in 1952 and by the Royal Family since 1862.
The Queen and the Duke of Edinburgh stay in the main house every Christmas with the rest of the Royal Family.