The force responsible for the Queen Elizabeth II's 20,000-acre estate at Sandringham, Norfolk does not have enough firearms officers to man all the shifts involved in 24-hour cover.
Police authorities are seeking to attract experts from forces in other areas while also training up some of its own existing officers, The Sun tabloid reported.
The huge increase in armed police would be needed to provide full-time security at the estate in Norfolk, where a 10-bed property is tipped as the couple's country home.
A spokesman for Norfolk Constabulary said recruitment of firearms officers "remains open to both internal and external candidates".
Besides guarding Sandringham, the new cops will do other duties round the county, the report said.