Poland internationals Wojciech Szczesny and Lukasz Fabianski are both sidelined with injury.
When asked if he would be signing an emergency loan goalkeeper, Wenger said: "No.
"We have a crisis because Fabianski got injured and will have surgery. He will be out for three months.
"We still have Mannone, and Szczesny comes back next week or in two weeks' time at the latest."