City has told the Italian club that it will not entertain any offer to take the Bosnian on a temporary basis with a view to a permanent switch next summer.
However, Roberto Mancini is willing to listen to offers for Dzeko as he looks to raise funds and create room in the squad to bid for Arsenal captain Robin van Persie.
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Milan wanted to take Dzeko on loan and pay his 215,000 euros-a-week wages in full - but City rejected its approach, just as it did when the Italian giants made a similar bid for Carlos Tevez in January.
The Premier League champions are also well aware that Milan received 65m euros following the double sale of Zlatan Ibrahimovic and Thiago Silva to Paris Saint-Germain last month.
Dzeko, who cost 34m euros and has three years remaining on his contract, has complained about a lack of first-team opportunities after finding himself out of the side for much of last season - but still managed to score 14 Premier League goals.
And he hinted at the possibility of a summer transfer at the weekend, speaking after City's 2-0 friendly win over Wolfsburg, saying: "I always follow the Italian league and one day I would like to play in it. I also know that Milan has sold two of its best players.
"For now I am a City player, but to be sure I will stay here I will have to wait until the end of the month. I'll see what happens, and if someone else comes in."
However, Mancini insisted on Sunday that he does not expect Dzeko to leave City this summer.
"It’s pretty unlikely he will leave,” the Italian told reporters.
"He is right to say it’s no fun being on the bench but when you join a big club then competition is normal."