They will offer the England winger a £200,000-a-week, five-year contract to move to the Etihad Stadium.
Roma have tracked Dzeko for some time and City have reportedly demanded £14.4m for the striker, although Roma have placed a starting bid of £9m.
Dzeko will be followed out of the Etihad exit door by Stevan Jovetic, who has failed to impress at City since his £22m switch from Fiorentina.
Jovetic is being chased by Inter, although the Serie A giants are also hoping to capture Mohamed Salah from Chelsea and are reportedly unlikely to move for both men.
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