Wenger, Arsenal's manager for over 20 years, is out of contract at the end of the season and has pledged to make an announcement about his future "very soon".
Ozil is currently stalling over a new contract, with his existing deal due to expire in a year, and suggested he will not make a decision on his future until he knows what Wenger is doing.
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"It's not just important for me, but for the whole club," Ozil told the Mail on Sunday. "It's important to know if he stays or if he goes. We need to think towards next season.
"He's very important. In my career I've always made decisions not just because of clubs, but managers too.
"As a footballer, it's important to have the manager's trust and believe they can develop you.
"When I went from (Real) Madrid to Arsenal, I came for him because I told him at the time he'd be my first option. That was the case. We still have a super understanding today.
"I have his trust, he's a superb coach. He's been successful for many years, he's been here for 20 years and has always managed to get Arsenal to reach the Champions League, making Arsenal a big club.
"He deserves to be shown respect."
Wenger is bidding to steer Arsenal into the Champions League for the 20th season in succession.
Ozil not panicking over Arsenal contract
His side trail Manchester City, who occupy the fourth and final Champions League qualifying spot, by seven points, but have two games in hand, beginning with Monday's trip to Crystal Palace.
Ozil, 28, said his decision on whether or not to extend his contract was not contingent on Champions League qualification.
"I haven't thought about that. The club comes first, not Mesut Ozil or anyone," he said.
"The team have the aim to reach the Champions League and I'll fight for that. In the summer we have enough time to talk about the future and we'll do that."
He added: "I'm very happy. I have a connection with the club. I love London, it's great to live here, but I can't say today what will happen in the future. In the summer we'll definitely talk."
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