The German playmaker has not gotten a look in since the league resumed after the COVID-19 lockdown.
Ozil is the highest paid player on the Gunners payroll, and Keown thinks it may be better for everyone if his contract is bought out.
Asked if he thinks Ozil has a future at Arsenal, Keown told Stadium Astro: "No, I don't think he does.
"And I think really this summer now they may see the player being paid off, because I think now it's about protecting the next generation.
"I think it's a real shame because he had a magnificent talent, but if you're not prepared to work hard out of possession for the team, then you don't get to play in the new Arsenal at the moment and that's what Arteta is all about.
"Work ethic comes first and then everything else is a bonus you play from there. Clearly he's not seeing enough on the training pitch.
"People go into comfort zones whether they like it or not, they can't often see it.
"But, you know, that must have played a part. He's a millionaire every month, after tax.
"My attitude to that is every player should get the best contract they can, and if he's performing he deserves that, but when he doesn't, it's very expensive for Arsenal football club.
"It maybe sends the complete wrong message to some of those youngsters, he's had opportunities he hasn't taken."