The Italian has kept two clean sheets while deputizing for the injured Wojciech Szczesny and Wenger feels he can challenge the Pole for a regular place with a solid performance
Wojciech Szczesny was making his first appearance for the Gunners since suffering a rib injury last month, but was forced off after with an ankle problem during the convincing 6-1 victory over Southampton on Saturday.
Mannone has performed well in goal for Arsenal so far this season, keeping clean sheets in both of his Premier League appearances against Liverpool and Stoke City.
And Wenger is confident that the former Atalanta trainee can repeat his impressive performances when the Gunners kickoff their Champions League campaign against Ligue 1 champions Montpellier.
"Vito is very close [to the Arsenal No. 1 jersey], and he gets another opportunity now," Wenger told Sky Sports News. "He has belief and he has the mental strength to deal with that."
Meanwhile, Wenger has praised Arsenal's opposition for their progress in the last few years, and warned that despite the club's lack of experience in the competition, Rene Girard's team could be the team to beat in Group B.
"What they did [last season] is a miracle because I think three years ago they were in the second division and one point away from relegation to division three," he said.
"It is difficult to know why they have not started well this season. Maybe because they were champions and now they are the team to beat.
"People have maybe a little less urgency and everybody is a bit more cautious against them."