The Sun says they will step up interest in £25million-rated Scamacca.
But if rival bids from the likes of Newcastle push the price up, the Hammers may turn their focus to Torino captain Andrea Belotti. Italy international Belotti, 28, is out of contract in the summer and so would not command a transfer fee.
Scamacca, 23 and 6ft 4in tall, is a man in demand thanks to a breakout Serie A campaign that has earned him his first senior caps for Italy.
He has scored 16 goals in 35 league matches but may well have played his final game for Sassuolo.
Opponents AC Milan and city rivals Inter are among the host of clubs considering a summer move for Scamacca.
He would cost at least £25m and Premier League interest could drive the asking price far higher.
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