The 25-year-old Italian, a £2m summer signing from Arsenal, played his part in Wednesday's 2-1 Capital One Cup fourth round victory over Southampton which handed the Black Cats another home tie against Chelsea in the quarter-finals.
Mannone replaced Keiren Westwood between the sticks with the Irishman still suffering the after-effects of his collision with Hull defender Paul McShane at the weekend, which left him slightly concussed and prompted his understudy's introduction as a substitute.
Mannone said: "Of course I want to keep my place, that's why I came here.
"I've been hurting on the sidelines, so I was really happy to take my chance on Saturday and do well for the team.
"It was a really good win last night and I was involved in a good performance. I want to push on.
"Obviously it's down to the manager but I'm available for him and I will push as hard as I can in every single training session and every single chance I get out there.
"This manager is very open to performances, he likes to watch the game and he will pick what he thinks is the best side.
"It's not down to me, the manager has an opinion. But hopefully I've done enough to show I can play in this team and I want to push on to be number one. That's why I'm here."
Watch Sunderland take on Manchester City live on Sky Sports HD1 (2.05pm kick-off) during Ford Super Sunday.