The 23-year old has been ever-present for the Gunners in the Premier League so far, establishing himself as Wenger's first choice in the process following an impressive start to the campaign.
The Poland international found himself briefly out of favour towards the latter stages of last season, but Wenger believes that Szczesny has similar traits to Lehmann which have allowed him to bounce back.
"I gave Lehmann as the example to Wojciech at that time. When I dropped Lehmann, he told me: 'I will force you to play me again'," Wenger told the Sun.
"Wojciech is an extrovert. He is a happy boy who likes to be funny and sometimes these people will get the reputation of not being serious.
"You always have to be careful with players who show too much self-belief but I think Wojciech questioned himself, especially after the European Championships in Poland last year, which were a massive disappointment for him.
"But every big player has to go through those disappointments and I believe he has matured as a result of what happened last year."
Arsenal were reported to be in the market for a new goalkeeper throughout the summer but, despite the loan signing of Emiliano Viviano, who is yet to make his debut, Wenger says it was never the plan to replace Szczesny.
"I was always convinced he would make it here and the speculation linking Arsenal with another goalkeeper in the summer did not come from me," he said.
"People forget that 23-years old for a goalkeeper is like being 18 for an outfield player and he has already played two full seasons in the Premier League and can only get better."
Wenger also defended the half-time comments of England boss Roy Hodgson, believing that whatever is discussed during the break should not be leaked to the public.
"Sometimes we can go a bit overboard at half-time. It's an emotional situation and there is a lot of effort and desire in there," he said at his weekly press conference.
"The old rule is that what happens in the dressing room stays there.
"Unfortunately, those times have gone, so today you have to be very careful what you say, wherever you are.
"Sometimes you can say one word that is not politically correct. That can happen to any manager. We would all like a bit more confidentiality and we know we're in danger in these situations."