Reports emerged on Wednesday claiming that the two teams were close to shaking hands on a big-money move, possibly worth up to £54m with various add-ons included.
Costa has been desperately seeking a return to the Spanish capital after falling out with manager Antonio Conte, who informed him via text at the end of last season that he is no longer wanted in West London.
A summer transfer failed to materialise, however, meaning that the Spain international instead has to wait until January at the earliest - when Atleti are free to register new players - before sealing a Stamford Bridge exit.
Atletico chief Cerezo insists that any talks will wait until the New Year, however, telling Diario AS: "If his family is moving [to Madrid] then I do not know.
"What I do understand is that Costa is a Chelsea player and until January, there is time to talk to his club and with anybody else. We will not do anything until January."