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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.