The base in Merchant Street is in need of repairs, and has restricted access for those with impaired mobility.
SPA members are being asked to approve proposals to relocate to Aberdeenshire Council's Buchan House premises in the town.
The building would be disposed of, along with the police office in Cruden Bay.
Meanwhile, an SPA meeting will also hear that plans to close the Aberdeen police control room and transfer calls to Dundee are on track.
The move is part of Police Scotland's cost-cutting plan to centralise control rooms.
Peterhead police station is to be relocated, under plans being discussed by the Scottish Police Authority.