Germany boss Joachim Low is now keeping close tabs - especially as Ivory Coast have made enquiries, as the player's father is from there.
When asked whether Gnabry had a chance to get into the German squad for Brazil next summer, Wenger said: "There is more than a small chance. There's a big chance.
"We are looking at a guy who has good individual talent, he can pass people, is a good finisher, and has a very good football brain with good vision. He has great pace. Two footed, can finish right and left. He has a lot in the locker.
"I am not afraid to play him. I have shown that against Tottenham in the FA Cup - it was a big game. He has convinced many people that he at least deserves another chance.
"He was influential in that game, and until now when I played him he has always had an impact on the game."