The Sunday Express reports that former Chelsea boss Carlo Ancelotti is keen to bring the 33-year-old to Spain.
Ancelotti is reportedly keen to offer the veteran defender a short-term deal.
Fabio Coentrao is expected to leave Real Madrid in January and Cole could move to the Spanish side cheaply as a replacement.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.