The Hammers are known to want a new forward to challenge Sebastien Haller and Ablian Ajeti upfront
Football Insider quoting a West Ham source claims the club has made a big-money move for the 24-year-old in an attempt to beat Spurs and Chelsea to his signature.
The Poland international striker is expected to leave Milan this month and is keen on a move to the Premier League.
The striker has lost his place in the Italians’ starting line up for the last three Serie A matches after failing to hit the form of his 2018-19 season.
Piatek scored five goals from 19 matches this season after netting 30 goals from 42 matches last season across spells with Milan and Genoa.