The Gunners will return from the international break with a trip to struggling Norwich on Saturday evening. Mannone, who looks set to again deputise for injured number one Wojciech Szczesny at Carrow Road, feels there is plenty more to come from Arsene Wenger's squad.
"The team is doing great, we have had [many of] the big games already," he told Arsenal Player.
"We had a few good wins and a few draws away, and not many other teams will get draws at Man City or a win at West Ham. It is not easy to win at Liverpool, as well.
"We have started the Champions League well too, the team has got a good base to kick on from. I am looking forward to some big achievements."
He added: "I have no doubt that if we keep our focus and we keep our mentality, it's not a doubt that we are going to challenge for the title."
Wenger will be hoping no more of his globetrotting squad return with injury after Theo Walcott was pole-axed by San Marino goalkeeper Aldo Simoncini at Wembley. He is back with the Gunners receiving treatment for what is understood to be a badly-bruised chest.
Walcott, who is yet to agree a new contract extension, is not anticipated to be involved for the trip to Norfolk, while full-back Bacary Sagna and midfielder Emmanuel Frimpong have both recently stepped up their rehabilitation, but this weekend could come too soon.
England midfielder Jack Wilshere, meanwhile, is set to play in a specially-arranged friendly with a Chelsea XI at Arsenal's training ground on Wednesday afternoon as he looks to sharpen his match fitness after more than a year on the sidelines - perhaps even with one eye on making the squad for the away Capital One Cup tie at Reading on October 30.
Elsewhere, Arsenal confirmed Pat Holland has left his role as Under-18s coach due to personal reasons, and will be replaced by Steve Gatting, who moves up from assistant professional development coach.