The story has been blown up out of proportion. I've read it few days ago on the German website. Nothing much has been said.
To summarize it, Dzeko has said that he's been somewhat disappointed that he spend majority of second half of the season on the bench and that he believes that he's quality player who should have played more. That led to him losing rhythm and that he started to doubt himself. He added that he respects the Coaches decision and he's fully committed to the City's 12/13 season and will do whatever it takes to help the team defend the Premier Leauge Title.
I am not sure how reliable SUN and rest of English Media is but the Sun report is really laughable.