He was offered £85,000 a week to stay at Stamford Bridge, which he turned down seeking a payrise to match the top earners at the club.
He was a peripheral figure towards the end of the season as Chelsea won the Premier League title and relations between him and the club have soured to the point that the original offer is no longer on the table.
Cole has turned down a move to West Ham, where he began his career, while Manchester United have been linked with a move.
Should United make an offer then Chelsea could be tempted into revising their stance to avoid losing him to their title rivals.
Tottenham Hotspur, where Cole would be reunited with manager Harry Redknapp whom he worked with at West Ham, would be an appealing choice while Liverpool have also been mentioned as an option.
Tottenham, with Champions League football to look forward to next season, would seem to be in pole position if they choose to meet his wage demands.