Andrea Pinamonti scored 10 Serie A goals for Genoa last season
Both clubs have inquired about the Italian’s availability, though talks are at an early stage.
Pinamonti scored 11 goals in all competitions last season on loan at Genoa, and the 26-year-old has aspirations of breaking into the Italy team.
The former Inter Milan forward has scored 26 goals across his last three seasons in Italy, earmarking himself as one of Serie A’s most reliable goal scorers.
Pinamonti, who also has interest from clubs in the Bundesliga, is keen on a move to the Premier League as he believes it will give him the platform to stake a claim for his first Italy cap since 2022.
The club, though, are adamant they don't want to lose both players in the same window.
Brentford, however, are still looking to add depth in forward areas, with the club also holding an interest in Ipswich winger Omari Hutchinson.
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Should Antonio leave, Graham Potter would only have one senior striker in Niclas Fullkrug available to him next season, and the club are therefore looking into the possibility of adding another forward to their squad.
There's been no direct club-to-club contact between Sassuolo and West Ham or Brentford, but both clubs have signalled an initial interest in Pinamonti.