The Italy international - who spent last season on loan with Juventus - is now close to a move to the Hammers and is expected to complete a medical today, according to Gazzetta dello Sport.
The Italian has spent most of his career in Serie A which has seen also seen him play for Cagliari, Genoa and Fiorentina.
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Alessandro Matri is expected to complete a medical at West Ham today
The one-time England international is working his way back to fitness following a knee injury and has returned to training but is unlikely to feature against Liverpool this weekend.
Slaven Bilic is looking to bolster his striker options and Zaza was an £11.5million target but Juventus pulled the plug on the move.
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Andy Carroll's talks with a move away from Upton Park have broken down
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Carroll hasn't played for West Ham since February 16.
The Hammers are also closing in on a move for Tottenham striker Emmanuel Adebayor.
The Togolese star was expected to join Aston Villa earlier this month but the move fell through and West Ham now look set to secure a deal.
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Emmanuel Adebayor has been linked with a move to numerous Premier League clubs this summer
The former Arsenal and Manchester City forward is expected to complete a medical in the coming days, according to talkSport.
Bilic is desperately searching for alternative strikers with Enner Valencia and Mauro Zarate both out leaving Diafra Sakho and Modibo Maiga his only options.