The striker is urging Tottenham's Croatian playmaker to move to Eastlands but declined to comment on his own future at the club after enduring a barren run in front of goal
The Spurs midfielder was subject to much transfer speculation last summer with Chelsea leading the pursuit, but the north London club turned down numerous bids for the player.
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Dzeko told SunSport: “Yes, everyone is after him but I would love it if he came to City. He would be a great addition.
“Besides that, he would have everything at City — Champions League, fighting for the title, great wages.
“I am cheering for him to choose City.”
Despite a rasping start to this Premier League campaign, the Bosnian’s form has dropped in the second half of the season and speculation on his own future has began to grow.
But Dzeko refused to speak definitively on his future in Manchester.
“There are still games left in the league and it is too early to discuss such matters,” he said.