The shot-stopper's form has come under the spotlight in recent weeks and he was criticised again on Wednesday following England's 4-2 defeat to Sweden in Stockholm.
"For me, Joe is the best keeper in England, absolutely," Mancini told reporters. "For me he is the first choice.
"But if he does not play well, I can change. I don't have any problem [doing this]."
City continue the defence of their Premier League crown on Saturday when they welcome Aston Villa to the Etihad Stadium.