The Bosnian star has been linked with a move away from Germany, particularly with a shift to Italy to join AC Milan but the club has now dropped their interest meaning that one of the English duo look certain to snap him up.
Dzeko has been prolific in the last two German Bundesliga seasons and has confirmed that he will be happy to go wherever the right offer comes from.
"I never said that I absolutely wanted Italy," he said. "If the right offer comes in then I will say yes.".
Dzeko's £25million asking price is believed to be too much for Milan but both Chelsea and City are right in the frame to pay this sort of money for the 24-year old who has also had interest from Manchester United and Tottenham.