Mannone has enjoyed a run in the Gunners' starting lineup due to an injury to first-choice keeper Wojciech Szczesny.
With perennial number two Lukasz Fabianski also out with a long-term shoulder problem, Mannone has started six Premier League matches already this season.
The Italian youth international told the club's official website that he is ready to stake a claim for a regular place in Arsene Wenger's plans.
He said: "I am trying to be the No 1 for this club and win trophies. That is my only concern and I would like to make that clear.
"The boss has given me the chance. I have to keep going and prove myself in every single game. This is my best time at Arsenal so I would crazy to not take the chance to put up a fight for my place.
"I am really happy and honoured to play for this club. I am loving every minute of each game. West Ham was a great win in a tough place and I was happy to give my contribution.
"I just want to tell everyone I am just trying do well and give something back to the fans who support the team as well as the boss who has given me the chance."
Mannone kept goal in the Arsenal team that produced a fine comeback to beat West Ham United 3-1 at Upton Park this weekend to maintain their unbeaten run away from home.