The 20-year-old Pole is frustrated at being behind Manuel Almunia, Lukasz Fabianski and Vito Mannone in the pecking order at Emirates Stadium, claiming he is ready to play at the highest level but that 'nobody is brave enough' to pick him on a regular basis.
Szczesny gained valuable experience on loan at Brentford last season, but is desperate for the chance with the Gunners, having not even made the bench for the Carling Cup tie at Tottenham.
Waiting game: Wenger admits he rates Szczesny but the young keeper will have to wait for his chance
Wenger, though, maintains Szczesny's time will come.
'He is right he deserves a chance but the keeper is in front of him, Mannone, deserves a chance as well,' the Arsenal manager said.
'You can only play one goalkeeper. It's part of their job as a football player to live with competition and decisions.'
Wenger continued: 'I believe the best thing for him is just to focus, work hard and trust us.
'No club in the world has started more players at the top, top level than we have. Nobody, so he is in the right club. But impatience is a characteristic of youth.
'What they forget when they are 20 is that they can play until they are 40, whereas a normal player can only go to 32 or 34 if it all goes well, so what they lose at the start they gain at the end of their career.'
The young Poland keeper is out of contract at the end of the season, and so would be free to talk to other clubs in January.
Wenger has every intention to retain Szczesny.
'When you educated a player like we do with Szczesny, who arrives at the age of 16, it is a long-term investment which costs a lot of money, so you want to keep the players,' he said.
'We will talk to him about a new deal. We rate him and we want to keep him.'
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