HITC Sport understands Coventry City are keen on League One rivals' manager.
The former Leeds United club captain's wage demands were too high.
Glasgow Rangers manager Mark Warburton spoke highly of former Ibrox striker Nicky Clark, says Bury boss David Flitcroft.
Bury have found the right men to guide them forward, on and off the field, and could by a Championship club by this time next year.
Lee Erwin joined Bury on loan from Leeds United earlier this month.