The 18-year-old’s current contract is set to expire in 18 months’ time.
Arsenal are ready to offer Wilshere double his salary and the youngster could be set to earn around £40,000-a-week on a new six-year deal.
Wenger said: “We are confident we will get Jack on a longer contract very quickly and hope we can announce it soon. He has had a great start to the season.
“There is a touch of Liam Brady about him although maybe Liam is not too happy about that!”