The Blues made Richards available for loan in November after the 21-year-old, signed from Ilkeston FC in December last year, failed to nail down a regular spot in Steve Burr's side.
Richards, who began his career with Derby County, will now link up with Steve Housham's National League North side.
Richards has made ten appearances so far this season and has scored once - the third goal in the 3-2 win over cross-border rivals Wrexham in October.
Meanwhile, Gainsborough have confirmed that Adam Drury has left the club by mutual agreement.