The Poland international has emerged as the Hammers’ top midfield target and they have been in talks with Napoli over a move for him.
West Ham saw the Serie A giants knock back their opening offer for Zielinski as it was deemed too low.
The Londoners are not prepared to give up their hopes of signing the midfielder and are gearing up to make an improved offer.
But it has been suggested that Zielinksi is not too keen on joining David Moyes side in the ongoing window and rather prefers a move to Lazio.
However, according to Italian daily Il Mattino, the 28-year-old is now seriously considering the possibility of signing for the Hammers as they have handed him a lucrative contract worth over €6m per annum.
Napoli coach Luciano Spalletti still sees Zielinksi as a key part of his plans at the club, but he is now thinking about leaving for West Ham.
An offer in the €35m range could help West Ham make a breakthrough in the negotiations with Napoli for the Pole and it remains to be seen whether they will manage to get a deal over the line.
