Darrell Clarke's side clinched third in League Two with a last-gasp winner on Saturday against Dagenham & Redbridge.
New Zealand forward Rory Fallon, 34, is to be released after making just three first-team appearances this season.
Defenders Lee Brown, scorer of the late winner over Dagenham, and Tom Lockyer already signed new contracts in April.
Having secured back-to-back promotions, securing top scorer Matty Taylor's services for at least another season would be seen as a major boost for the club if he was to agree a new deal.
After Saturday's victory, the striker told BBC Radio Bristol he would speak to club's president regarding a new deal.
Chairman Steve Hamer has said the club will have the chance to match offers made by other clubs for Taylor this summer.
Promoted Bristol Rovers have offered new contracts to all but one of their senior professional players after their dramatic finish to the league season.