The existing building in Barnwood will be demolished to make way for the new purpose-built centre.
EDF energy plans to redevelop its former offices in Barnwood into homes and new offices.
The football club says it has fallen victim to vandals multiple times since moving to its new base.
The structure is said to have been found along with two buildings and the grave of a woman.
Plans for a 49.2 ft (15m) mast next to a church and arboretum would impose on the wildlife, he says.
The man said he was shouted at by another dog walker at Barnwood Park and Arboretum.
