The Germany international has emerged as the Gunners’ latest target in recent days, with Arsene Wenger understood to be looking for an enforcer to follow the arrival of Alexis Sanchez.
Rumours in Spain have suggested that the Londoners are ready to pay big, but now it appears that the cost of a potential raid will be too high.
Real want in excess of £20m for their star, who would command wages of around £150,000-per-week.
With Khedira now in the final year of his contract the fee Los Blancos are demanding is seen as too steep by Wenger, who may now alter his focus towards Lars Bender.
The north Londoners have already paid north of £30m for Sanchez and are set to shell out another £10m on Mathieu Debuchy, which is rumoured to have taken up the majority of their summer budget.