The 23-year-old midfielder is a key target for Manuel Pellegrini this summer.
As the Hammers hope to battle for a Europa League place, they see Fornals as someone who can add much needed creativity to the midfield.
According to Sky Sports, Villarreal want £31 million for the Spanish star.
West Ham are pursuing other targets as well as Fornals, as they hope to have a midfield signing wrapped up in the next ten days to two weeks.
Fornals played 35 games in La Liga last season, managing two goals and three assists from a primarily central attacking midfield position.