The 23-year-old, who continues to be linked with Paris Saint-Germain, was in strong form for his Italian club during the 2021-22 campaign, scoring 16 goals and registering one assist in 36 Serie A outings.
According to the Evening Standard, West Ham are currently in talks with the Serie A outfit over the possibility of bringing the centre-forward to the London Stadium.
The report claims that Sassuolo value Scamacca in the region of €50m (£42.3m), which David Moyes's side would allegedly be prepared to spend to bring him to the English capital this summer.
Meanwhile, according to the Daily Mail, Southampton are keen to bring Tottenham Hotspur midfielder Harry Winks to the club during this summer's transfer window.
The report claims that Winks is surplus to requirements at the Tottenham Hotspur Stadium following the arrival of Yves Bissouma from Brighton & Hove Albion this summer.
Southampton allegedly view the Englishman as a leading target and are preparing to launch an offer, but the Saints could face competition from a number of other clubs.
The 26-year-old, who has dropped out of England contention due to his struggles last term, has played over 200 times for Spurs in all competitions during his professional career.
Elsewhere, Nottingham Forest allegedly want to further boost their squad for the 2022-23 campaign by bringing in Lewis O'Brien from Huddersfield Town.
According to The Telegraph, Forest are hoping to secure a deal for the 23-year-old, who has spent his entire professional career with the Terriers.
O'Brien has made 131 appearances for Huddersfield in all competitions, contributing eight goals and 10 assists in the process.
There have been suggestions that he is valued in the region of £10m, and Leeds United are also believed to be interested in signing him as a replacement for Kalvin Phillips.
Forest have already been busy this summer, as they prepare for a return to the Premier League, with the likes of Taiwo Awoniyi, Neco Williams and Dean Henderson arriving at the club.
Meanwhile, over in Italy, it has been reported that AC Milan defender Fikayo Tomori is close to signing a new contract with the Italian champions.
The centre-back enjoyed a strong 2021-22 campaign for Milan following his arrival from Chelsea, making 40 appearances in all competitions.
There has recently been speculation surrounding the England international, with Manchester United thought to be keen to bring him back to the Premier League.
However, according to Italian journalist Fabrizio Romano, Tomori is discussing a new long-term deal in Milan, with the defender determined to stay at the club 'for many years'.