Wenger has been unemployed since he left the Gunners in 2018 and turned down the Bayern job last November.
As Arsenal coach, Wenger oversaw Gnabry’s departure from the academy in 2012 and the winger made 18 appearances under the Frenchman.
After a failed loan move to West Brom, Gnabry was sold to Werder Bremen in 2016 for just £ 5m and joined Bayern a year later.
The German set Europe on fire with his dazzling performances and helped the Bavarian giants to achieve a historic triple last season.
Bayern boss Hansi Flick was the mastermind of Bundesliga, DFK Cup and Champions League triumphs, but Gnabry insists Wenger would also be a hit at the Allianz Arena.
“I believe him [Wenger] could succeed? For sure. He has shown that he was a fantastic manager to run a club, “said the 25-year-old.
“I would tell the difference [between Wenger and Flick] For me, as an older player, it’s probably easier to communicate with the coach.
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“When you just walk in and are very young, you are sometimes a bit shy, but technically they are both on a very, very high level.”
Some of Gnabry’s best performances last season were in the Champions League, where he scored nine goals in ten games.
In a famous performance, he scored four goals after former rivals Tottenham in north London when Bayern took the lead with a 7-2 group stage win.
Gnabry added, “The biggest thing about seeing some of my friends is, they give me a lot of motivation.
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“When you know the history and the atmosphere in the stadiums, of course it’s great to play in England, but in a way, my Arsenal history gives you more motivation against Spurs.
“Besides that, every game is important and it went well for me against London teams.”
Gnabry has scored four goals in five Bundesliga games this season, while leaders Bayern are about to make a close trip to second-placed Borussia Dortmund on Saturday evening.
Gnabry turned his attention to the classic and said: “It’s very important because it’s the two best teams in the Bundesliga that play against each other.”
“Whoever emerges as the winner will hopefully gain a lot of confidence from this game for the rest of the season.”
“As we know how important this game is internationally, a lot of people will see the game. That makes it more valuable to us. ”
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