Wenger has previously stated that Wilshere must prove his fitness in order to be offered a new contract, and the midfielder has successfully come through 90 minutes in the club's last three Premier League fixtures.
A report has claimed that Wilshere is looking for a pay-rise to commit his future to the North London outfit, and Wenger has hinted that it could be a factor in whether the England international stays at the Emirates Stadium.
The Frenchman told reporters: "We will sit down with him. I believe if he can meet a point of agreement financially, he will want to stay."
Wilshere has previously indicated that he would like to extend his stay with a club he has been part of since beginning his time in the youth setup in 2001.