The Premier League club rebuffed interest in the Bosnian in January but they will be willing to sell a player with just over a year left on his contract at the end of the season.
The Premier League outfit dismissed all interest in the Bosnian during the January transfer window but is now willing to sell the striker at the end of the season if it receives what it deems an acceptable offer.
Dzeko will have only one year left on his contract in the summer and will be in a strong position to negotiate a cut-price move.
The 27-year-old, who joined City from Wolfsburg in January 2011, is likely to be available for around 18 million euro, although he will want to join a club who can at least match his 130,000 euro a week wages.
Dzeko was the subject of an inquiry from Tottenham last December, while Arsenal are also long-term admirers, but the player made an agreement with City chiefs that he would not consider a move until the end of the season.
The forward is also being closely monitored by a collection of continental clubs led by Inter, Borussia Dortmund and Napoli.
Dzeko has slipped behind Sergio Aguero and Alvaro Negredo in the forward pecking order at City but has still scored 17 goals in 36 matches in all competitions this season.
He has spoken of his frustration with not being a regular starter at Etihad Stadium, and the intense competition for places within Manuel Pellegrini's squad means he is likely to move on in the summer.
Dzeko will be part of the City squad that will attempt to overturn a 2-0 first leg deficit in its last 16 Champions League second-leg clash against Barcelona on Wednesday night.