Arsenal had been hopeful that the England star would be back in time to face the Premier League straggler but his comeback from an ankle injury has been delayed.
The 21-year-old pulled out of the England squad ahead of the World Cup qualifying double-header against San Marino and Montenegro after suffering from a recurrence of the ankle injury that kept him sidelined for 16 months last season.
Despite strongly denying reports concerning the playmaker's fitness over recent weeks, Wenger has admitted that he could be sidelined for some time.
"Honestly, is very difficult to say [when he will be back] - maybe in two weeks," he told reporters. "It is an inflammation of his bone, and we have such history with him so we are a bit more cautious. We have deferred his rehab by one week. We gave him one more week rest because it was wise medically to do it. We will rest him when it is needed. He knows he has to take care of his future. He is a very young player, he accepts it.
"He doesn't need any special treatment. You just have to be cautious with the inflammations of his ankle at times. He has been out for 17 months, so he wants to play. I understand that. If he is selected [to play for England this summer], he will go. It depends what kind of shape he will be in. If he has no problems, why not?"
The Frenchman also explained that Theo Walcott, Kieran Gibbs and Abou Diaby are likely to join the midfielder in missing out on Saturday's clash with Reading.
"Wilshere will still be out. [Theo] Walcott is injured, [Abou] Diaby has a problem we will have to check and [Kieran] Gibbs has been ill," he said.
"We have a good relationship [with England]. Walcott's injury was an accident."
Wojciech Szczesny was recently forced to apologize for his father's public criticisms of Wenger, but the 63-year-old dismissed suggestions that the goalkeeper would be moved on as a result.
"He's nearly played 100 games for this club," the manager said of the shot stopper. "That is fantastic. He has a very good future and has accumulated a lot of experience."