The Gunners boss is under increasing pressure to spend big this summer and with just over a week left of the transfer window, has set his sights on the Germany international.
Wenger has missed out on a number of top targets so far such as Stevan Jovetic, Gonzalo Higuain, Luis Suarez and Karim Benzema, but is prepared to splash the cash to land Ozil.
Arsenal are also interested in Ozil's team-mate Angel Di Mairia, and while Madrid are prepared to enter talks over a deal, the Argentine isn't willing to join the North Londoners.
Ozil, 24, was one of Real's key players for two years but questions have since been raised over his Bernabeu future due to the expected arrival of Gareth Bale from Tottenham.
The Welshman would likely take Ozil's spot in the Spanish capital, leaving the former Werder Bremen man out in the cold.
Meanwhile, Wenger, whose only signing so far this summer has been Yaya Sanago on a free from Auxerre, has accused the media of "brainwashing" fans into thinking there is a crisis at the Emirates.
Arsenal lost their opening Premier League game 3-1 at home to Aston Villa but responded by beating Fulham by the same scoreline at the weekend.