The World Cup winner has been out of action for six weeks after suffering a tear in his left thigh muscle.
Khedira has been heavily linked with a transfer to Arsenal in recent months.
The Gunners were thought to be interested in bringing the Germany international to Emirates Stadium over the summer but a move failed to materialise.
The midfielder has also been linked with a January transfer to Chelsea in recent days.
Khedira posted a picture of himself working in the gym earlier this week, along with the message: “Working hard on strength and power! can’t wait to join my team! Hala Madrid! Sk #strength #power #nike #work”
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