The 27-year-old Bosnia and Herzegovina international was told by City boss Manuel Pellegrini that he would be his main striker for the Premier League campaign shortly after he was appointed as Roberto Mancini's successor in the summer.
However, things have not panned out that way for Dzeko, who has struggled for first-team action due to the form and blossoming partnership of Sergio Aguero and summer signing Alvaro Negredo so far this term.
As a result Dzeko, who joined City from Wolfsburg in 2011 and has scored 33 goals in 84 league appearances, is thought to be pondering his future at the Etihad Stadium.
Dzeko's ten goals in the World Cup qualification campaign ensured Bosnia reached their first ever World Cup and it is being reported that he wants regular first-team football so he will go to the tournament in Brazil firing on all cylinders.
According to Corriere dello Sport both Inter, who want a long-term replacement for Diego Milito, and Roma are keeping tabs on Dzeko's situation and could make a firm bid for him in the New Year if he continues to struggle for first-team football.