The German international's contract is due to expire in 2018 but the Gunners are keen to get him tied down to a new one and talks are currently taking place.
Ozil is attracting plenty of interest from elsewhere with reports claiming his former club Real Madrid are keen to take him back, while Bayern Munich have also been mentioned.
However Wenger believes he will stay at the Emirates Stadium, even though there is still some talking to be done.
“I don’t think he needs convincing. He wants to stay here. But if you have a good bank, call me," Wenger quipped.
“It’s not just money. Arsenal can win titles of course. But that’s what we have to show. We are in a league where Man City, Man United, Liverpool, Tottenham, Chelsea everybody fights and you cannot guarantee that to anybody.
“We keep that (negotiations) discreet. At due time we will come out with that. We want to keep our best players, of course. But the more I say that, the more he is in a stronger position!”