Ex-York man Danny Racchi has been offered a two-year deal by Kilmarnock following a successful trial.
Bury manager Alan Knill is expecting Stephen Dawson to leave the club rather than sign a new contract.
A number of trialists will link up with the Bury squad for pre-season training on Monday.
Ben Futcher and Richie Baker have signed new deals to stay at Bury, while Danny Racchi has agreed terms.
Bury have offered Richie Baker, Danny Racchi and Cameron Belford new deals, while Ben Futcher is staying.
Bury have completed the signing of Danny Racchi, as first revealed by skysports.com on Friday.
Skysports.com understands Danny Racchi has secured a deal at Bury after impressing manager Alan Knill.
Danny Schofield, Chris Brandon and Frank Sinclair are among nine players released by Huddersfield.