The Bosnia international's future at the Etihad Stadium was the subject of speculation in the summer with several clubs credited with an interest.
But Dzeko claims he never considered moving away from the Premier League club during the summer transfer window.
"I think there was a lot of speculation from journalists but I never heard from the club they wanted to sell and you never heard from me that I wanted to leave," said Dzeko.
Dzeko also hailed the influence of new boss Manuel Pellegrini for his fine start to the season after scoring four goals.
"I've said it before; the manager is very important and for every player it's important to know the manager believes in him," added Dzeko.
"He gives confidence that can change everything."