Reports in France claim the 26-year-old is wanted by two of Europe's biggest spenders, as the German international has fallen down the pecking order at the Santiago Bernabeu.
A move to Chelsea is unlikely however, with Real Madrid reluctant to do business with former boss Jose Mourinho, having fallen out with the Portuguese tactician towards the end of his tenure in the Spanish capital.
Despite that, Mourinho remains on good terms with a number of their players, and reports have also linked Diego Lopez with a move to west London.
The bookmakers have slashed their odds on Chelsea making a move for Khedira, making the Blues 4/6 favourites to land the former Stuttgart star.
Mourinho is on the lookout for reinforcements ahead of the new Premier League season, which kicks off this weekend.
Chelsea host recently-promoted Hull City on Sunday, before Aston Villa make the trip south just three days later.
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