Cerezo confirmed Chelsea have made contact but have not agreed to meet the buy-out clause for the Brazilian-born striker, who was part of a dismal World Cup showing from Spain.
The forward has long been linked with a big-money move to join Jose Mourinho at Chelsea, but Cerezo maintains the deal is far from complete.
"We don't know anything about Costa, all we know is that Chelsea have made contact but we haven't received any money or anything else yet," Cerezo said.
"Until we receive the money from his buy-out clause, he remains an Atletico player."
Costa, 26, spearheaded Atletico’s attack in a memorable season in which they won La Liga and reached the Champions League final under Argentine manager Diego Simeone.
Atletico have a history of losing their marquee players with Fernando Torres, Sergio Aguero and Radamel Falcao all having left the club in recent years.
The Atletico president admitted it is very difficult to say no when the biggest teams in Europe come calling.
"We've always tried to convince our players to stay, but the difference between our finances and that of other clubs is very large," he said.
Cerezo also confirmed Belgian goalkeeping star Courtois, who has been on loan to Atletico for the past three seasons, is set to return to Chelsea.
"Chelsea can count on Courtois, because he is their player," he said.
That will set up an enviable dilemma for Mourinho as he will have to choose between Courtois and long-time first-choice goalkeeper Peter Cech.
In addition to the likely departures of Costa and Courtois, Atletico have bid farewell to David Villa, who has signed for Melbourne City, and Tiago Mendes, who is out of contract.
Brazilian defenders Filipe Luis and Joao Miranda have also been linked with moves away from the Vicente Calderon Stadium.
Atletico have a ready-made replacement for Luis if he does depart after signing highly-rated left-back Guilherme Siqueira from Granada.
"That's the way football is," added Cerezo on the changes the La Liga champions will undergo this summer.
"We will try and get new players to come in who can score more goals or save more goals than the ones that are leaving."