Rumours of an impending £35million move for the 6ft5in 23-year-old striker had intensified over the weekend, especially with West Ham reportedly pulling out of their pursuit of Chelsea's Armando Broja, for the time being, and missing out on Jesse Lingard.
The Italian media have reported that Scamacca with now travel to West Ham on Monday or Tuesday next week to visit the club, agree terms and complete a medical.
The Italy striker, who has seven international caps, could be West Ham's fourth transfer of the summer if he signs on the dotted line, and comes as West Ham also chase the signature of Eintracht Frankfurt winger Filip Kostic.
Carnevali told Corriere dello Sport: "There's an agreement with West Ham for €36m fee plus €6m add-ons and 10% sell-on clause.
"I'm sure he will do great things, he's a huge talent and very good guy."
West Ham have been desperate to add an additional striker to a squad that has been totally reliant on Michail Antonio as a lone striking option for over a season.
The 32-year-old Antonio has not had a great pre-season and missed a number of chances in the second half in Saturday's friendly against Luton, including a one-on-one with the keeper where he failed to hit the net from the edge of the area.
However, West Ham fans will be cautious about welcoming a big-name striker into their hearts, as the club have a history of signing 'flops' from Europe.
Sebastien Haller, Felipe Anderson, Albian Ajeti, Lucas Perez, Simone Zaza and Jonathan Calleri have all felt the anger of West Ham fans over the last handful of seasons. So they will be hoping Scamacca doesn't add to this list.