Former Manchester City chief Pellegrini was hoping to entice his former striker to the London Stadium, but according to Calciomercato.com, Dzeko would prefer to stay in Italy.
The pair won the Premier League title together in 2013/14, but reports suggest that Dzeko was not Pellegrini's biggest fan.
In an interview with The Guardian, he described working the the Chilean in one word - 'OK' - and refused to elaborate when asked to.
The Bosnian forward looks set to leave Roma after four seasons at the Stadio Olimpico, with Inter Milan reportedly leading the queue for his signature as they aim to replace Mauro Icardi – likely to leave after a tumultuous campaign – this summer.
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