The Germany international has been a decisive figure since his move to Arsenal from Real Madrid in what was then a club record £42.5m deal in 2013.
Ozil was signed to help the Gunners end their long title drought but the World Cup winner hasn’t been able to help Arsenal improve their league performances.
The Arsenal star has won three FA Cup titles with the north London side but Ozil has often been accused of going missing in the club’s biggest games.
The German star signed a new lucrative contract with Arsenal in February to resolve the uncertainty surrounding his future at Arsenal.
Arsene Wenger is set to stand down as manager at the end of the season after another disappointing campaign under the 68-year-old.
Arsenal are on the lookout for a new manager amid speculation linking the Gunners with Massimiliano Allegri, Thomas Tuchel and Patrick Vieira.
Former Irish defender Cunningham believes Ozil needs to be shown the exit door when the next Arsenal boss takes over the reins.
“For the new manager coming in, he is one of the first players you want out the door,” Cunningham told Irish radio station Newstalk.
“It’s going to be difficult because he is on such a huge wage. You’ll probably have to pay him to leave the club.”
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