Wilshere, 21, returned from more than a year out injured in October, but is already being heralded as an integral part of the future hopes of both club and country.
Arsenal head to Tottenham on Sunday, where they will come up against in-form Bale, who has drawn comparisons with Europe's best after his match-winning performances this season.
Wenger believes his own talented midfielder has everything ahead of him.
"Bale is the flavour of the moment. When you look at Wilshere, who will deny that this guy will get 100 caps for England? Nobody, if he has no injury," said Wenger.
"My worry is not to compare Wilshere with anyone else. My only worry when you are a footballer player of that talent is to become as good as you can become.
"That is the only thing that is of interest to me. I leave the comparisons to other people. My job is to get the best out of him."
Wenger feels it is sometimes overlooked just how much Wilshere has achieved since arriving at the club aged nine.
"You tend to forget how old he is when you see him play. You never come out of a game and think 'this guy is 21 years old'. He's at a stage where the others have not started," said Wenger.
"You think of Jack (as) an established player in the Premier League and at international level, that is still something special."
Wenger feels Wilshere will develop into Arsenal's natural leader. He continued: "Jack breathes football. He doesn't talk too much, but he understands everything.
"What he has exceeded is the speed of his physical fitness in the game. Honestly, I never expected that."
Wilshere has yet to score in the Premier League this season, but Wenger feels that the goals will soon come.
"I believe it's part of his development to play a bit more advanced," the Arsenal boss said.
"In some games, he is more comfortable deeper. I believe he has a little dribble that can get him through in the final third and the finishing will come.
"He's a bit in a situation like (Cesc) Fabregas was for a while. He said to me 'but I cannot score goals', however you could see that it would come.
"Jack doesn't talk about it, but who doesn't want to score goals? He is more a team player than a goalscorer.
"He will never be a goalscorer, but he can be capable to score."
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