The 21-year-old midfielder earned rave reviews for his impressive midweek performance for England as the Three Lions beat Brazil 2-1 in Wednesday’s friendly at Wembley.
And Wenger is sure that the England international, who has made a successful return to action this season following a lengthy injury lay-off, will stake his claim as one of the world’s top talents in years to come.
“The most important thing for me will be to keep his passion for the game, and keep the attitude of wanting to become a better player.
“If he keeps these two ingredients – which is not always easy – he can become a fantastic player. He already is one, but he can become one of the best in the world.”
Wenger is also backing Wilshere to establish himself as one of England’s most important players.
The Frenchman added: “The influence he has today on the England national team already is absolutely fantastic – let’s just hope that he does not have any more injury problems in the near future. I believe he can handle all the rest.”