The 17-year-old German youth international has already made three first-team appearances for the Gunners since bursting onto the senior scene this season.
Those displays have indicated what a bright future the former Stuttgart product could have in the game after showing glimpses of his vast potential.
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And Wenger has backed his young star to make a name for himself in future.
He told The Sun: "He's 17 years old and has a lot of talent. Like all 17-year-olds, it's a bit too easy at that stage but the talent and personality are there.
"With the rest he just has to learn his job — that at this level you have to master all aspects of the game, of being a football player.
"But you see that he has the talent to make a good career."
Gnabry moved to Arsenal from Stuttgart in 2011 at the age of 16, and after breaking into the first-team will be looking to push on and prove his manager right.