Bury have offered a new contract to striker Mike Grella along with three other players.
The 25-year-old American scored four goals in 10 appearances for the Shakers since arriving on a short-term deal from Brentford in February.
Manager Richie Barker has also offered new terms to Andrai Jones, Luke McCarthy and Ben Futcher, the latter in a combined playing and coaching role.
Youth teamers Liam Boswell, Jordan Melia, Christian Dibble and Dalton McLaughlin have been offered their first professional contracts.
Heading out the exit door are Patrick Cregg, Andy Haworth, Ritchie Branagan, Zachary Rothwell and Danny Hudson, who have all been released at the end of their contracts.