The Hammers held talks with Villarreal over a £35million move for the Netherlands star earlier this week.
However, manager David Moyes is believed to have reservations about signing the former Bournemouth star.
West Ham are still waiting to hear if Jesse Lingard will accept their contract offer to join on a free transfer.
The England international, 29, enjoyed a successful loan spell at the London Stadium in 2021 and will not renew his contract at Manchester United this summer.
talkSPORT understands the Hammers are reluctant to meet Lingard's wage demands of around £150,000-a-week.
Moyes is keen to strengthen his attacking options and provide extra competition for Michail Antonio, Jarrod Bowen and Pablo Fornals.
Another player who looks unlikely to join West Ham is Southampton captain James Ward-Prowse.
The England midfielder has been linked with a £25m move to east London.
But talkSPORT's football correspondent Alex Crook insists Ward-Prowse will not be going anywhere over the coming months.
West Ham are looking to make their third signing of the summer having already landed Nayef Aguerd from Rennes and Alphonse Areola, who was on loan with the club last season, from Paris Saint-Germain.