The 25-year-old, who featured for Italy at EURO 2016 and missed a penalty as the Azzurri were eliminated by Germany in the quarter-finals, was a target for the Hammers last summer, but a loan move for his signature ended in disappointment.
West Ham are once again on the lookout for a centre-forward this year, and although Carlos Bacca is their major target, the Colombian is stalling on a deal, so there is every chance the Irons may miss out on the 29-year-old.
And reports claim that the Londoners are preparing for disappointment, with Zaza once again on their radar.
The 25-year-old has struggled for game time since his 2015 move to Juventus from Sassuolo, and only managed 19 Serie A outings (just five of these were starts) last term, yet he notched five goals in the process.
The 6ft. 1” marksman had a respectable record at Sassuolo, notching 20 goals in 64 league appearances for the Reggio Emilia-based side.