The Gunners midfielder, who will see his current contract expire this summer, has been offered fresh terms by the club on a lower weekly wage than his previous deal.
It is understood the 26-year-old is not happy with the terms on the table and is hoping Arsenal improve their offer while also looking at options elsewhere, with Everton, West Ham and Wolves reportedly keen.
Wenger says he is not worried about the lack of movement on talks over Wilshere's future and believes it is only a matter of time before the situation is resolved in a positive manner.
Wenger said: "I can't give you any news because I don't know really what is in his mind.
"I can just update you on saying that he has not signed. He has an offer for a long-term contract and we want him to stay. I hope at some stage he will sign it.
"I am always confident. As a club you want the players to stay and be paid well and I think everyone would agree we pay our players very well."