The 25-year-old struggled for goals last season after his arrival from Wolfsburg in January but has been lifted by a fine strike in last week’s Community Shield and the opener against Swansea.
Dzeko said: "The beginnings have always been slow for me, and that was the case at City, but this year I feel fit and I feel very good. I feel much better than last season.
"For every player it is important to be fit and have a good pre-season behind him. This summer I have done everything with the team and that makes you feel better.
"I want to improve in every game, but I have started the season well. I try to do my best in every game to help the team."