Ozil appears set to end his association with the Gunners with his lucrative contract due to expire in the summer.
The German's situation has Arsenal fans split, but Keown isn't impressed with the 32-year-old - pulling no punches in a scathing assessment.
He told talkSPORT: "It hurts me that a player of that talent can't get on the football pitch, it's a crying shame
"For me, he doesn't go down as a legend, because he doesn't match the energy and determination of legends that I've seen at that football club.
"If he had [Kieran] Tierney's determination, coupled with that ability, he might've gone down as the best player ever to play for Arsenal.
"He's become calculated in the way that he's undermining the club with tweets, and I think it's now time to go."
Keown continued: "Two-and-a-half years ago when Atletico Madrid knocked Arsenal out of the Europa League, I watched very closely and it felt like he [Ozil] was conning the fans.
"He wasn't giving everything for the shirt; I accused him of crocodile tears, it felt like something was very wrong. That was two-and-a-half years ago, and my opinion hasn't changed.
"There was a session of illnesses, a mystery back injury, away games he wasn't available.
"Is there a problem with the player? Is he conning us? Eventually he'll write a book and we'll get to know the whole story," he added.
"But if you've got that much talent and you're not getting picked, you can't be giving 100 per cent, and that was happening two-and-a-half years ago.
"He [Dr Sogut] accused me of jealousy and not being worthy; I think the 449 games for Arsenal qualify me, I'm not sure how many the agent has played.
"My eyes don't lie. Statistics tell you an amazing story about Ozil, which I don't think is convincing."
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