The Hammers are currently in fifth spot in the Premier League table with eight games remaining, and they sit just a point adrift of Manchester City in fourth place.
With the potential of sitting at Europe’s top table next season, Slaven Bilic is considering reinforcements in the summer, and Dzeko is firmly in his plans.
The 30-year-old has struggled in the Italian capital this season, scoring just nine goals in 33 appearances in all competitions.
As a result, he could be interested in a return to England where he won a league title with Manchester City in 2014, with West Ham offering to allow Roma a chance to recoup their initial outlay on the Bosnian international of around €17 million.
While the appeal of a move to London would be strong for Dzeko, the forward would also be left to regret leaving Italy after just one season of struggles.
If Luciano Spalletti is willing to give him another chance to impress next season, then the conditions and contract terms will allow for him to stay and try to prove himself in the Italian top flight.
Having already enjoyed success in Germany and England, the towering striker will be keen to replicate that in Italy with the Giallorossi, and so for the time being his agent will not consider any proposals before it is confirmed which clubs will compete in the Champions League next season.
Adapted from an article in La Gazzetta dello Sport by Chiara Zucchelli