Miralem Pjanic has been saying he'd like him in Italy
The Bosnian forward has played a big part in City's two title successes over the past three years, with his goals usually being vital in terms of the outcome of games.
His team-mate for Bosnia, Roma's Miralem Pjanic, has been quoted saying: “Dzeko has told me that he likes Italy.
“And I think he would be a coup if we signed him.”
The President of Inter Milan has also expressed his admiration but said that they can't afford players like Dzeko today.
It would seem an odd move if City were to part with their Bosnian forward, especially given the vital contribution he made to the side last season - which is no doubt the main reason they are trying to tie him down to a new contract.
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He may have played second fiddle at times during last season when Alvaro Negredo was in form, and developing a seemingly formidable partnership with Sergio Aguero, but Dzeko was the man who filled the void and stepped up to the mark as both strikers picked up injuries during the season.
It is hardly surprising that other clubs are interested in him as he averaged over a goal every two games in the Premier League last season, and probably of little wonder that his team-mates for his country are trying to lure him away from City towards their own clubs.
But the best thing City can do is try and tie him down to a long-term contract, because at the age of 28, his best years could still be ahead of him, and they wouldn't want to lose him prior to that.