With skipper Thomas Vermaelen set to sit out today's FA Cup fourth-round tie at Brighton with an ankle problem and his deputy Mikel Arteta sidelined by a calf injury, the 21-year-old England midfielder could well start with the armband at the Amex Community Stadium after being handed it by Vermaelen in the midweek Barclays Premier League win over West Ham.
"Jack will be captain of this club one day, first of all, because of the quality of the player. There is also his commitment and desire to win, his understanding of the game. Jack senses on the pitch what you have to do," Wenger said.
"He is naturally a guy who is not scared of anything on the football pitch and that is usually the sign of a leader. Jack wants to win and shows you that.
"So of course he will be one of the leaders of this club - in fact he is already on the pitch. A leader is somebody who does everything on the pitch to help his team to win, and Jack does that."
Wilshere has certainly shown his leadership qualities, looking to lift Arsenal during what has been a testing recent spell which included successive Barclays Premier League defeats to Manchester City and Chelsea before the midweek masterclass against the Irons.
Wenger, though, stressed Wilshere's career must not be fast tracked.
"It is important that the player gets to the stage where he develops first completely into an accomplished football player and then takes responsibility to take care of other people," the Gunners boss said.
"Once you know you can perform in every game, then you can take care a little bit of other people."
Despite beating West Ham, Arsenal remain in sixth place in the Barclays Premier League, with their target now breaking back into the top four rather than any talk of a sustained assault on the title.