Herman van Holsbeeck, the Belgian club's sporting director, confirmed the Premier League side, Valencia, Sevilla and Red Bull Salzburg were all tracking the defender, who can also play in midfield.
After winning the Belgian top flight with Anderlecht, the 24-year-old is set for a fresh challenge and has also been linked with Arsenal.
The Senegal international is under contract until the summer of 2016, leaving Anderlecht in a prime position to dictate proceedings with the club reportedly seeking 10million euros for the centre-back.
"We have had talks with Sevilla, Valencia and Salzburg, and West Ham have contacted us," Van Holsbeeck told Estadio Deportivo.
"We want to make the best possible decision and sell from the most profitable aspect for us, although we take into account the opinion of the player."
Kouyate made 38 appearances in Anderlecht's successful Pro League campaign this term.