He found his way to Bayern via Werder Bremen and has since blossomed in Germany, hitting the headlines after a blistering four-goal salvo in his side's 7-2 victory against Tottenham in the Champions League last week.
Wenger, though, has hinted that there may have been foul play at work to lure him away from north London.
“We tried to extend his contract for a very long time and I think that Bayern manipulated behind the scenes, that if he went to Bremen he would join Bayern after,” he told beIN Sports .
“He was always a very talented boy who lacked confidence in some stages, but we always thought we had a player who could achieve a lot.
“He came back from a very bad experience on loan at West Brom where his confidence was destroyed. I tried to rebuild him because I believed in him.”
Wenger has counselled the 24-year-old, who has scored 18 times in 51 outings in all competitions for the Bavarians, that he should not feel that he is the finished article in the game, however.
He said: “A top-level career is consistency, if you look at the players that dominate our sport it’s the ones that show huge consistency and that’s what is it at stake. Can he maintain the quality of performances that he showed the other night?”
While the former Arsenal manager was impressed by Bayern’s performance against Spurs, he did not necessarily see it coming.
“Bayern had just won 3-0 at Paderborn, you wouldn’t expect them to come and put seven goals away at Tottenham,” he said. “I think it was one of those nights where everything goes for you and everything against Tottenham.”
Niko Kovac’s side currently lie third in the Bundesliga standings, despite having scored 20 goals in their opening seven matches. They are two points behind early pace setters Borussia Monchengladbach.