The French international has been heavily linked with a move to Manchester United this summer.
Last week when he was asked to give a number out of 10 regarding the possibility of a move to Old Trafford, Griezmann replied: "Six."
However, Cerezo is adamant that Griezmann will be playing in Atletico's new Wanda Metroplitano stadium next season.
Cerezo told Marca: "Griezmann will stay here. Not here at the Calderon, but at the Wanda."