The 26-year-old, who joined from Wolfsburg last January, is once again being linked with a move away from the club, despite an impressive start to the season, with City seemingly scouting around for striking reinforcements.
"Every time I see a paper, for what seems like a year or more there is a story saying that I am leaving City, or that I want to go," Dzeko said in The Sun.
"But I've never said that so the stories don't come from me. I've always wanted to stay at City and fight for my place.
"My motto has always been 'Never give up'."