The Hammers are reportedly targeting a loan deal with the option to purchase the forward at the end of the spell.
The Hammers are keen to add further forward options to their squad before the transfer window closes having lost Enner Valencia to a long-term injury before the start of the campaign.
That has left them with just Diafra Sakho to lead the line, with Andy Carroll still on the injury list and Modibo Maiga not favoured, although he did manage a goal in the loss to Bournemouth on Saturday.
That has led them to Italy, and Juventus forward Simone Zaza, who only joined the Italian champions this summer for £12.75m from Sassuolo but is not, as yet, fancied by manager Massimo Allegri.
It is believed the Hammers will pay £2.1 million to secure the Italian for the season, with the option to purchase him completely for £10.8 million at the end of the loan spell according to Sportmediaset.
With Juve also adding Paulo Dybala and Mario Mandzukic to their ranks this summer, Zaza is unlikely to feature much in the first team, despite having scored 11 goals for Sassuolo last season.
A loan to West Ham makes sense then given their reduced numbers up front, and that area being one the fans and manager Slaven Bilic are keen to see improved before the end of the transfer window.