The Gunners have been eliminated from the Champions League and fallen seven points behind Premier League leaders Liverpool in recent weeks.
It has been suggested that Wenger will wait until the summer before weighing up his options, but Szczesny believes that the Frenchman will remain at the Emirates Stadium.
"I don't have any doubts about his future," Szczesny told the Daily Telegraph. "The boss has been around for so long, had so much experience, I'm sure he's been through times much worse.
"We believe in him, he believes in us and I'm sure he'll work for a long time."
Arsenal drew 1-1 with Manchester City in their last outing on Saturday.