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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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