Sullivan has disclosed that Tottenham made a move for Kouyate, who can play as a midfielder or a defender.
The West Ham co-chairman, though, has made it clear that the 26-year-old will not be sold in the summer transfer window.
“Spurs came on for Kouyate,” Sullivan told The Mirror. “They said: ‘What would you take for Kouyate?’ We said we’d take Harry Kane. Silence on the other end of the line.”
“We wouldn’t sell Kouyate,” added Sullivan. “He is not for sale. He signed his new contract and he came out like a tiger the following day. He is a huge man, a real athlete, very fit. A very good player.”
Kouyate has been on the books of West Ham since the summer of 2014 and has a contract until June 2021.
The Senegal international is an important player in the West Ham midfield and has done well this season.
The former Anderlecht man has scored five goals and created 19 chances in 31 Premier League appearances this campaign.
Kouyate has a pass accuracy of 79% and a shot accuracy of 52%, and has won 80 headers, 25 dribbles and 67 tackles.