Reports in Spain suggest that Real are desperate to cash in the midfielder, who is in the final year of his contract, this summer rather than lose him for free to Bayern next year.
The Gunners have spent nearly £60m already this summer after tying up deals for Alexis Sanchez from Barcelona, Mathieu Debuchy from Newcastle, David Ospina from Nice and Calum Chambers from Southampton.
While the German World Cup winner Khedira would slot seamlessly into the Arsenal midfield, it has been reported that he favours a return to his homeland.
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