The Gunners manager says the Poland international has the potential to become a vital part of the history of the north London club.
The Poland international endured a tough time last season and found himself dropped by Wenger for the first time since establishing himself as the club's No. 1. However, he soon returned to the team and has been in impressive form this season, keeping his 50th clean sheet for the Gunners when they saw off Marseille 2-0 in the Champions League on Tuesday.
And Wenger feels that, at just 23 years old, Szczesny is only going to get better.
"Yes, he can be one of the best," the manager told Arsenal Player. "You have to question a little bit the defenders as well (when you consider clean sheet stats) because you're part of a team and sometimes too many individual stats can lead you to conclusions that are not as obvious as that.
"But what I am sure is that he has the potential to be a historical goalkeeper for Arsenal Football Club. That will depend on how much he will continue to focus, to have the desire to be better, to have the desire to put the hard work in. If you look around at different clubs you see how quickly a goalkeeper can lose confidence, how quickly a goalkeeper can lose all his qualities. The level of urgency in this position has to be absolutely 100 percent.
"He is a very young man. I personally believe his composure is better, his reading of the game is better, his level of concentration is much stronger and that comes out with his numbers. He is still a very young goalkeeper because he's at an age where other goalkeepers start to play.
"He has already a vast experience. That's why I think it's very good news for the club that he has extended his contract. But rightly so as well because this club has given him a huge chance at a very young age - and that is not common at the top, top clubs."
Meanwhile, Wenger has given an update on the fitness of Lukas Podolski and Alex Oxlade-Chamberlain ahead of his side's trip to Cardiff City on Saturday.
Podolski, who has been out since August with a hamstring injury, is not set to return to the first team for another three weeks. Oxlade-Chamberlain, meanwhile, is likely to be back from his knee injury in the new year.