Dzeko arrived in England from Wolfsburg in January 2011 when Manchester City paid £27million for him.
And while the Bosnian international took his time to find his feet, he racked up 72 goals in 189 appearances for the club despite often playing second fiddle to Sergio Aguero.
But he was loaned out to Roma last summer and having made sufficient appearances for the first team the Serie A club were obligated to make the move permanent.
Dzeko has scored 10 times in all competitions for the Italian side and has started to attract attention from some of Europe’s top sides.
According to Italian outlet ForzaRoma, with proven Premier League goal-scorers hard to find both Everton and Liverpool have made enquiries about his availability.
Christian Benteke is expected to be one of those on the way out and with Daniel Sturridge apparently still not over his injury concerns, a striker will be high on the German manager’s list of priorities.
But their city rivals could also be in the market for a forward this summer.
Romelu Lukaku is expected to be a target for a number of Champions League clubs and Everton, who are currently without a manager, will need to replace the 18 league goals he scored this season.