The Italians have drawn up a shortlist which includes Marseille striker Loic Remy and Internacional's Leandro Damiao.
Both are wanted in England with Newcastle maintaining interest in Remy and Tottenham hopeful of signing Brazil international Damiao at the third attempt for around £15million.
City are reluctant to sell Dzeko without finding a replacement first.
Edinson Cavani at Napoli is one target but the Italians' excessive valuation of £50million is proving prohibitive.
City assistant coach Angelo Gregucci: "I don’t know if the club will lay siege to Napoli for Cavani, but every club with a player of the highest level will know they’ll be courted by bigger clubs.
"Mancini decides the transfer targets along with the new directors. If you ask the clubs who can afford Cavani, for example Real Madrid, Bayern Munich and Manchester United, then I think they’d want Cavani just as Manchester City want him. If he should want to undertake a new adventure, then he will tell the club and I expect they’d let him go.
"Cavani is among the world’s top five strikers and is doing great things. Napoli invested heavily in him, but the player's intentions are decisive."