A host of teams are being linked with the Brazilian-born front-man, who is hoping to feature for Spain at this summer's World Cup finals.
Costa has had a superb campaign for Atletico, with 21 goals to his name - just one off Real Madrid superstar Cristiano Ronaldo.
Chelsea are widely reported to be very keen on landing the 25-year-old, who was the subject of a bid from Liverpool last year.
Cerezo admits that he is expecting interest from clubs, but he does not think that will lead to a sale.
"I don't believe Diego Costa is leaving the club next season, we won't sell him next season, but that won't stop other clubs from wanting him," he said during a sports forum at the Complutense University of Madrid.
Costa has been linked to a possible swap deal with Chelsea, who could possibly offer current Atletico number one Thibaut Courtois - on loan from the London club - or Rojiblancos legend Fernando Torres.
But Cerezo insists that they would not entertain swapping him either.
"Undoubtedly we don't want to use any player as a bargaining chip for some other player. You can see this in that we never sell but other teams come for our players," he added.
"Diego wants to play with the Spanish national team and that has been an important decision.
"He likes Spain, lives here, and believes it is better for him."
Atletico Madrid's technical director Andrea Berta added: "We are a company and in order to keep functioning properly, must sell each year.
"However, we believe we can keep our players for at least one more season."
Courtois has been linked with Real in recent days, but Cerezo feels that has come about because of the derby which is this weekend.
"We always have the same problem when there is a match against Real Madrid, I don't know why," he said.
"It has happened to Fernando Torres, Sergio 'Kun' Aguero and Radamel Falcao.
"I can say that he has a contract with us until the end of season.
"As everyone knows, Courtois belongs to Chelsea and he signed for five years with them and has been with us for three."