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 Welshman Gareth 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, and he said: "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."
He added: "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."
There were reports on Saturday night that an Arab consortium is considering making a bid for Arsenal in the near future. The Sun on Sunday and Sunday Telegraph both reported the interest, with funds for the bid said to be coming from Qatar and the United Arab Emirates.
American Stan Kroenke is the club's majority shareholder, while Uzbek Alisher Usmanov also holds a significant stake. The offer for Arsenal would reportedly see the potential investors bid around £20,000 per share, making Kroenke's holding worth £830million.