Wenger is under intense pressure to leave The Emirates after yet another season without a league title challenge, embarrassment in the Champions League and a struggle on their hands to finish in the top four.
Ozil, whose own contract has a little over a year left to run, wants the Frenchman to stay.
"It's not just important for me but for the whole club," Ozil told the Daily Mail. "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 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."
The German World Cup winner believes the club needs to sign big players in the off-season.
"I think the club know they need to strengthen," he said. "But what's most important is the manager's opinion. He and the club will make the decision.
"When you look at our squad, it's not as broad as Bayern's or Real Madrid's. In the Champions League, that's not enough, especially against big teams, because they have more breadth in their squad."