The Gunners handed Ozil a new contract rumoured to be worth £350,000 a week at the Emirates Stadium last month to secure the World Cup winner’s long-term future at the north London club.
Arsenal lost five of their last six games in all competitions ahead of Thursday night’s trip to AC Milan following defeats by Tottenham Hotspur, Oestersunds, Manchester City and Brighton.
Ozil struggled to impress during the five losses to heap pressure on the World Cup winner, especially since his lucrative new long-term contract with the north London club.
The German midfielder has been regularly criticised for his subdued performances in the Arsenal team during some of their most difficult results in recent seasons.
Former Gunners defender Keown urged Arsene Wenger to omit Ozil from the Arsenal team if the north London side are to get themselves out of this current slump.
“Wenger will always pick Mesut Ozil but I am not sure he is the right player to get them out of this situation,” Keown told the Daily Mail.
“Ozil needs to dig deep and if he is not going to, then he should not be playing.
“I want to see the Arsenal player who is taking this bad run personally and digging out his team-mates who are not working hard enough.”
Ozil moved to Arsenal in a £42.5m deal from La Liga giants Real Madrid in the 2013 summer transfer window.
The German star has won three FA Cup titles during four and a half seasons at Arsenal.
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