The Pole is in line for a recall with Lukasz Fabianski suffering a rib injury.
Wenger said: "I have total confidence, no matter who starts the game against Everton.
''In the past I have shown that I trust these players, and no matter who plays they will show their quality. Szczesny has handled not being in the team really well.
''He has worked very hard and has handled the situation in a positive way."