EPL Champions, Chelsea have agreed to a double deal with Roma for Bosnian striker Dzeko and Brazilian left-back Emerson Palmieri which could rise to £52m with bonuses included.
Dzeko has been thrashing out personal terms and is set to agree at a deal worth £140,000 a week, compared to his current £80,000 in Italy.
And he is understood to have been reassured by boss Antonio Conte that he will not be seen just a back-up to £58m Morata, who joined from Real Madrid in the summer.
Despite being 31, Dzeko has thrived in Italy since he joined Roma from Manchester City in August 2015.
He has been directly involved in 64 Serie A goals – 46 goals, 18 assists – and privately is believed to be shocked Roma are willing to let him go.
But although his overall record may be excellent, Dzeko has been having a lean time himself of late.