Hammers boss David Moyes is on the lookout for attacking reinforcements this summer, to provide competition for Michail Antonio, and Scamacca is believed to be one of his top targets.
The 23-year-old enjoyed a prolific 2021-22 campaign in front of goal for Sassuolo, scoring 16 times in 36 Serie A appearances.
Carnevali has previously revealed that the club have held talks with Paris Saint-Germain's sporting director Luis Campos over the potential sale of Scamacca.
The Neroverdi chief has since confirmed that both PSG and West Ham have made offers to sign the striker, with the Hammers tabling a higher bid.
Speaking to reporters, via journalist Fabrizio Romano, Carnevali said: "West Ham are offering €40m for Scamacca and Paris Saint-Germain offering €35m.
"There are also some add-ons as difference. We don't need to sell, so we will see - there's no agreement with any club now."
It remains to be seen whether PSG will make a higher offer for Scamacca as they are now on the verge of signing former Newcastle United target Hugo Ekitike for a €30m fee plus add-ons.
The 20-year-old is currently undergoing his medical, as reported by Romano, and Reims president Jean-Pierre Caillot has also confirmed the deal, stating that the club are "happy to let Hugo fulfil his dream" with PSG.
Ekitike's move to the Parc des Princes could now pave the way for West Ham to strike a deal with Sassuolo for Scamacca, who is valued at €50m (£42.5m).
While Sky Sports News are claiming that Scamacca would like to join PSG this summer, stating that he has gone public to push the Ligue 1 champions into raising their €35m offer, the striker is seeking regular first-team football next season, which he may not be guaranteed with the French giants.
The prospect of becoming a key player under Moyes at West Ham, however, could tempt the Italy international into moving to the London Stadium this summer.
It is thought that the Hammers still hold an interest in Chelsea striker Armando Broja, who has been linked with a host of other European clubs amid uncertainty over his long-term future at Stamford Bridge, while they are also in the market for a new centre-midfielder and a left-back.
Moyes has so far added three new players to his ranks this summer, signing goalkeeper Alphonse Areola centre-back Nayef Aguerd and midfielder Flynn Downes for a combined fee close to £50m.