The 21-year-old is set to wear the armband against Brighton on Saturday, as regular skippers Thomas Vermaelen and Mikel Arteta may be rested at the Amex Stadium
Goal.com revealed on Friday that the 21-year-old will be handed the armband for Saturday's FA cup clash against Brighton with Mikel Arteta and Thomas Vermaelen set to be rested.
“I think Jack will be captain of this club - yes, of course,” Wenger said.
“First of all, because of the quality of the player. Second, his commitment and desire to win. And his understanding of the game. He understands football very well and senses on the pitch what you have to do.
“Jack is naturally a guy who is not scared of anything on the football pitch and that is usually the sign of a leader. He wants to win and shows you that.
“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 he does that.
“The potential is there [to be England captain], of course. But I’m not national team coach - you should ask that question to Roy Hodgson, who will be happy to talk about it.”
Wenger admits he has not decided on the captain for his side's clash against Brighton but claims Wilshere would be in the frame.
“I haven’t decided that [captaincy] yet. Vermaelen made that choice on Wednesday and I let him make it." said Wenger.
“At the moment, for me, we have two captains: Vermaelen and Arteta and, after them, occasional captains. On the day, why not? He [Wilshere] can be, yes.”
Arsenal have not won a trophy since the 2005 FA Cup and the 63-year-old has challenged his side to prove their ability in the FA Cup, as well as in the Champions League.
“It is important because people will look at us,” Wenger added. “How we respond to a challenge like the FA Cup. We wanted to do well in the Capital One Cup. After what happened [at Bradford], of course it’s important for us to show we are ready and motivated.
“It is important to go for every trophy we can. It is not the only trophy. We are in the Champions League. I know you have already kicked us out but we will surprise you against Bayern Munich!
“We will take it seriously. You know I won four times the FA Cup because I take the competition seriously.”