The Bosnian striker has been linked with a move to Italian giants AC Milan as City are keen to sign Robin van Persie from Arsenal, pushing Dzeko further down in the pecking order.
Dzeko disclosed at the weekend that he would like to play in Serie A at some stage in his career, but Mancini has indicated that it will not be next season.
"I'm pleased, as this means we have good players, but it's pretty unlikely he will leave," he told Sky Sport Italia.
"He is right to say it's no fun being on the bench, but when you join a big club then competition is normal."
Mancini also gave his view on the Serie A title race in 2012-13, while claiming that Manchester United are favourites to win the Premier League title this season.
"Juventus are the team to beat, not just because they won the Scudetto, but also thanks to their reinforcements," said the Italian.
"As for the Premier League, Manchester United are in pole position."
City will begin the defence of their Premier League title with a home game against Southampton on Sunday, August 19.