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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?