The Hammers are pressing the accelerator in the transfer market and are working on deals for Sassuolo striker Gianluca Scamacca and left-sided Eintracht Frankfurt man Filip Kostic.
David Moyes wants more fresh faces in through the door though and West Ham are keen on Poland international Zielinski.
He is on the books at Serie A giants Napoli and according to Italian journalist Ciro Venerato on Rai Sport, West Ham have now kicked off talks to sign him.
The Premier League side, who initially phoned Napoli about the player, have indicated a willingness to spend around €40m on snapping up Zielinski.
However, Napoli want to earn €50m if Zielinski is to be sold.
Zielinski has another two years left to run on his contract at Napoli and the Italians are clear about his valuation.
He has made over 280 appearances for Napoli, scoring 40 goals, and has won the Coppa Italia at the club.
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