The 26-year-old forward has been in and out of the City first-team this season despite being the club’s top goal-scorer with 13 goals in all competitions.
Borussia Dortmund have been linked with a move for Dzeko, with Robert Lewandowski poised to leave the German champions at the end of the season.
And Citizens manager Mancini has refused to rule out a possible departure for Dzeko, admitting that the Bosnia-Herzegovina striker needs regular football.
“We haven’t spoken about the transfer market because there are 10 games to go but in June anything can happen,” Mancini said.
“For me, Dzeko is a great player but he is the type of footballer who needs to play all the time. In Italy he could score 20 goals a season but he would cost someone €20m (£17.4m) and maybe more.”
“United will now concentrate all their strength to win the championship and it was hard enough for us before this game against Madrid,” he said.
“It was better for us that they stayed in the Champions League.”