Metro reports that Madrid boss Carlo Ancelotti has told his scouts that Ramires is one of his targets for January.
Ancelotti is keen to bring in a new box-to-box midfielder and have been linked with a number of such players in recent weeks.
Ramires joined Chelsea when Ancelotti was in charge at Stamford Bridge and reports suggest the midfielder would be keen to link up with his former boss again.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.