The Gunners have bid £24million for the midfielder and negotiations are in the advanced stages, claim the Metro.
Having wrapped up a sensational deal to bring Alexis Sanchez to the club already, Arsene Wenger looks set to continue his spending.
The club have made signing a centre midfielder a priority, and fans will be delighted that another big name looks set for the Emirates.
The news of the clubs' advanced talks comes after talkSPORT's Stan Collymore tweeted information on the deal.
The former Liverpool man wrote: "Spoke to agent. Arsenal in advanced talks with Sami Khedira. F**k me, they're getting serious."
With just 12 months left on his current deal in Madrid, Khedira's asking price shouldn't be an issue for the Gunners.
Khedira - who previously played for Stuttgart before turning out at the Bernabeu - has rejected a new deal and is widely tipped to leave the club this sumer.
The German is also said to prefer North London to any other destination with close friend Mesut Ozil, as well as international team-mates Per Mertesacker and Lukas Podolski, already at the club.
One potential snag will be the burly midfielder's wage demands.
It is believed Arsenal would have to pay at least £150,000-a-week to land their man - making Khedira the highest paid player at the club.
The wage would eclipse record signings Ozil and Sanchez who are believed to earn closer to the £140,000-a-week mark.