The 32-year-old has two years to run on his current contract, and the Serie A giants could decide against an extension, with his age and salary being key reasons.
Dzeko has been in fine form since leaving the Premier League for Roma in 2015, netting 78 goals in 148 appearances so far.
The Bosnia and Herzegovina international, who has a record 55 goals in 97 games for country, is a huge goal threat and will definitely improve West Ham greatly should a deal be reached.
Pellegrini’s side have managed to find the back of the net just eight league goals in as many games this season, and they could really do with an experienced and top goalmachine like Dzeko.
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