The Gunners manager is confident that the 21-year-old will progress his career in a more advanced role on the field, expecting that the midfielder will reach 100 caps for England
The 21-year-old has yet to find the back of the net in the Premier League following his return from injury last October and the Gunners boss feels that finding the target will be the next step for the England international's progression.
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"Jack doesn't talk about it but who doesn't want to score goals? I believe it's part of Jack's development to play a bit more advanced. The finishing will come. Jack is more a team player than a goalscorer but he can score and he will score.
"He will be a 10-15 goal player. My only worry for a footballer of Jack's talent is to become as good as you can become. My job is to get the best out of him."
Arsenal head into Sunday's derby with Tottenham four points behind Andre Villas-Boas's side, who sit in fourth, and, while the Frenchman admits that the focus is on Gareth Bale, he reserved praise for his own midfielder.
"Bale is flavour of the moment but look at Jack Wilshere – who will deny he will get 100 caps for England? Nobody if he has no injury," Wenger added.
"You tend to forget how old Jack is when you see him play. This is a guy who is 21 – it's a stage where the others have not started. You think of him already as an established player in the Premier League and at international level. He is something special."