The former Newcastle and Manchester United forward is out of contract on Wearside after spending only one season at the Stadium of Light.
He made only eight appearances, including just three starts, all in December against fellow strugglers Derby, Reading and Bolton, before being sent out on loan to Burnley at the end of last season.
Cole turned down a chance to join the Clarets on a permanent basis but could be more tempted by the offer from Gary McAllister.
Cole is one of the leading scorers in Premiership history in a productive career that began at Arsenal and continued at Bristol City, Newcastle United, Manchester United, Blackburn Rovers, Fulham, Manchester City, Portsmouth, Birmingham and Sunderland.