Challinor had a further 12 months remaining on his deal at Edgeley Park but has ripped up the contract by mutual consent.
The 28-year-old had failed to convince Hatters manager Sammy McIlroy of his merits and will now seek out a new club.
League Two outfit Bury will be hot favourites to land the former Tranmere player after Challinor spent three months on loan at Gigg Lane last season.
Challinor recently admitted he is keen to return to The Shakers and is likely to commence discussions with the club in the near future.
Bury boss Graham Barrow revealed he has been waiting for Challinor to resolve his situation at Stockport before launching his effort to sign the experienced stopper.
Barrow told the Bury Times: "The problem with the Challinor signing has been between him and Stockport County but thankfully that seems to be getting sorted out now."
