Slaven Bilic is desperate to add another striker to his ranks after Andre Ayew and Andy Carroll both suffered injuries.
It now looks like the Hammers may be in talks to sign Zaza from Juventus, after the players father confirmed that this was a possibilty for his son.
"West Ham are a solution we'd appreciate and represent something more concrete," he told Mediaset Premium.
"We'll have to see what Juventus do and we expect news soon.
"We are taking London into serious consideration as his next destination. Simone still has four years on his contract and would happily remain in Turin to give his contribution".
It also seems that West Ham may have an edge over Serie A sides, as Juventus do not want to sell the striker to a rival club.
"Juventus don't want to sell Simone to a direct rival. Milan, Napoli and Roma would be the options, we'll see what happens," his father added.
Would Zaza be a good signing for West Ham?