Rovers have to leave their current home for 18 months while a £30 million redevelopment scheme turns The Gas Stadium into an 18,500 capacity all-seater arena.
Cheltenham have indicated that revenue that a ground share could bring would become a welcome addition to the League One clubs finances.
Other alternatives include Bath City's Twerton Park which was a former home for Rovers, but Team Bath currently have a contract play there until 2009.
Swindon Town's County Ground is the only other 'local' stadium with the facilities to host Football League games.