The 23-year-old recently underwent a medical at London Road, but following discussions over personal terms, he has decided to return to the Globe Arena.
"Jack's a good talent. We're only too pleased to have him back. We accepted it because it was a decent offer, but he looked at it and, at this stage of his life and career, it wasn't the right move for him," Morecambe manager Jim Bentley told BBC Radio Lancashire.
Redshaw has scored once in four outings for the Shrimps this season.