With Gianluca Scamacca in their bag, the Hammers are looking to do more summer shopping in Serie A by trying to sign Zielinski.
They were initially prepared to offer a fee of €25m plus potential add-ons but that was not enough to make Napoli say yes to the move.
The Serie A giants are open to selling the Poland midfielder but want more money in order to allow him to depart.
And according to Italian daily Corriere dello Sport, West Ham are now prepared to table a new bid to convince Napoli to sell.
It has been claimed that the Hammers are prepared to offer a deal worth up to €36m to entice Napoli into letting Zielinski go this summer.
The figure is still short of Napoli’s asking price but West Ham feel a compromise could be on the cards.
Zielinski himself is still not sure about wanting to join West Ham and initially rebuffed their approach.
But West Ham have reportedly offered him a lucrative contract offer worth €6m to move to the London Stadium this summer.
