Wilshere is understood to be close to agreement after being offered a new incentive-based deal, with his existing one due to expire in the summer.
However, Wenger is less confident over Aaron Ramsey, who still has 18 months on his agreement.
Wenger said: “I'm positive, because I want him (Wilshere) to stay. I do the maximum I can to make him happy.
“Aaron is a little bit different because he has less time-constraints than with Jack. With Jack it is now. With Aaron, do we lose two weeks or three weeks, it doesn't matter much.
“I want him to stay as well… if he starts to score more hat-tricks!"