Chelsea are the early pace setters this season after winning all three of their opening games against Burnley, Leicester and Everton - scoring 11 goals in the process, and have strengthened significantly in the transfer window.
City themselves had a good opening two games with a win away to Newcastle and defeating last season's runners-up Liverpool at the Etihad Stadium, only to lose at home to Stoke City.
The Bosnian also mentions this weekend's opponents along with Liverpool, Tottenham and Manchester United as potential challengers for the league title this season.
Dzeko told the official Manchester City website: “As with every season, there are several teams that will battle for the title of champions in England.
“This season Chelsea might be the most serious challenger, but we mustn't ignore Liverpool, Tottenham, Arsenal, or United, who will certainly be much stronger than last year.
“After all, everyone has gotten stronger, and everyone wants to be first.”
Arsenal will have expected a little more from their start. They have picked up five points from their opening three games with a solitary win against Crystal Palace on the opening day, came from two goals down to draw with Everton at Goodison Park before being pegged back by Premier League newboys Leicester City.
Tottenham won their first two games before losing to Liverpool, who have also taken six points from their opening three games - whilst Manchester United have struggled to two points from their opening games, but have made some eye-catching signings in the summer in the hope they can help restore them towards the summit of English football.
The bookies would agree with Dzeko's assertion that Chelsea are the biggest threat to Manchester City landing a third Premier League crown in four years, with the other sides expected to fight it out for the remaining two Champions League places - though some commentators and pundits have suggested that Liverpool are likely to challenge after finishing as runners-up last season