The Spain international has long been linked with a big-money move to Chelsea, as the Stamford Bridge club seek to bolster their strikeforce ahead of the 2014-15 Premier League season.
However, Cerezo insists the London outfit are yet to meet Costa's buy-out clause.
"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 is quoted as saying by Sky Sports.
"Until we receive the money from his buy-out clause, he remains an Atletico player.
"We've always tried to convince our players to stay, but the difference between our finances and that of other clubs is very large."
Cerezo also appeared to confirm Belgium goalkeeper Thibaut Courtois would return to Chelsea after three seasons on loan at Atleti.
"Chelsea can count on Courtois, because he is their player," he added.
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