The Spaniards have been linked with the energetic midfielder for some time, with manager Carlo Ancelotti believed to be a big fan of his abilities.
Despite having spent around £150m over the summer, the La Liga side are still keen to make further additions to their squad.
Ramires is one of their top targets, and they are hopeful that Chelsea may be tempted to allow him to leave if Khedira is made a part of any deal.
Blues boss Jose Mourinho is said to be a big fan of the German international, who is rumoured to be unsettled at the Bernabeu.
The 26-year-old himself is keen to reunite with ‘The Special One’ after working under him at Real.
Los Blanco see a part-exchange deal as the best solution, and may make such a proposal this January.
Although Ramires is believed to be happy in London, Real are confident that they can lure him to the Spanish capital with a lucrative contract and a good chance of competing for domestic and European honours.
Would a swap deal involving Ramires and Sami Khedira be good for Chelsea?
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