The Daily Star says Khedira is available for £20m with Real Madrid ready to cash in after being unable to thrash out terms to extend the 27-year-old midfielder's contract beyond next summer.
And while Arsenal are ready to match that asking price, their unwillingness to offer a wage package which would eclipse top earners Mezut Ozil and new signing Alexis Sanchez has offered Chelsea a glimmer of hope.
Boss Mourinho is understood to have made a personal call to Khedira following Germany's extra-time win over Argentina to try and persuade him to sign for him for a second time.
Offering more attractive personal terms would not represent a problem.
But Mourinho knows he must offload players if he is to continue restructuring his midfield.
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