Wilshere, 20, has missed the whole of the season with a foot injury and Wenger admits that he is now worried about more disappointment.
Wenger said: "That is why I do not want to set the Olympics as a target because I do not know whether he will be fit to start at the beginning of the season. It is our target to get him to improve.
"When we start pre-season on July 9, if he can join in, then we have won the battle. But that is not guaranteed."
Wenger was pressed on whether there is no guarantee about starting next season and he added: "No. He makes slow progress and at the moment is still in a rehab centre. We take time, we are patient with him. He makes progress, but slow progress."