The Italian spent the second half of the campaign on loan at Hull City but has been required in goal at the Emirates Stadium in recent weeks following injuries to Wojciech Szczesny and Lukas Fabianski.
"He always believed in himself and was ready to show me that but he had no real opportunity to play," said Wenger.
"When I sent Mannone to Hull, I watched him every single game and all the reports I had were very positive. I was quite surprised no club went for him because I would have let him go."
Mannone signed his first professional contract with the Gunners in 2006 after arriving as a trainee from Atalanta.