The Poland international is in only his first full season as ‘No 1’ at Emirates Stadium and Wenger already feels he is one of the best in the Barclays Premier League.
The Frenchman believes Szczesny can become the best, but only if he continues to strive to improve as he has done so far.
"He is one of the best already in his first season [in the starting line-up]," the manager told the official club website.
“He has, like the team I must say, a promising future. We are confident that if he keeps his attitude and determination to do well he can be one of the best.
“My secret belief is that he shouldn't set any limitations on his progress and personally I am confident that he can let other people judge how good he is.
"I have shown with my decisions that I am a great believer in Wojciech. The rest, how far he can go, I wouldn't like to predict. That is what a career is all about."
After mentioning some of his attributes, Wenger warned the 21-year-old ‘keeper that he must not take his progress for granted and should continue to work hard.
“He is just at the start of his career though and you do not want to say too early that he is the finished article,” cautioned Wenger.
“I believe that as soon as you lose that sharpness to improve you are in trouble, no matter how young you are.
“That's why I would just say, 'keep your attitude and you will have a bright future'.”