The Daily Mail reports that Cole has failed to agree terms on a new contract with the Blues.
Cole will not sign a one-year extension with the club and is ready to hold talks with clubs such as Real Madrid and Paris St Germain in January.
Manchester United boss Sir Alex Ferguson has also been alerted by the availability of Cole next summer.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.