Hammers chief Sam Allardyce travelled to Belgium over the weekend to watch the Senegalese star in action after tracking him over the course of the past few months.
The talented and versatile enforcer has been a long-term target for Arsenal, with rumours having suggested that the Gunners have been in contact with the 24-year-old’s camp ahead of a potential summer swoop.
But West Ham are hopeful that they can beat their local rivals to Kouyate as they plan for the possible loss of Winston Reid – who is wanted by Tottenham.
Anderlecht beat Standard Liege 2-1 with the powerful defender starting the tie in a holding midfield role.
The Belgian side are rumoured to be willing to take around £8m for their man, and the Irons are hopeful that regular playing time may boost their hopes of tying up a deal.
As well as Kouyate, Allardyce was also taking notice of Michy Batshuayi.
The Liege forward is another target for Arsenal and has also been linked with Everton.