Commenting on reports in England that Brazil-born Costa, who has the same agent as Chelsea manager Jose Mourinho, had passed a medical and the London club had paid the buyout fee, Cerezo suggested the deal was some way from being finalised.
"Diego has the attributes to become the world's best forward but what we will not do is oblige someone to play where they do not want to," Cerezo was quoted as saying in Spanish media.
"If he (Costa) has an agreement with someone then let him come and tell us," he added.
"If he wants to leave, let him come and deposit his buyout clause which I believe is around 42 or 43 million euros."
An Atletico spokesman said later on Wednesday the Spanish champions had "no knowledge of anything that is being said" in the English media.
Costa netted 36 goals in all competitions for Atletico last season, helping them secure their first La Liga title in 18 years and propelling them to the Champions League final, where they lost to city rivals Real.
Costa is in the Spain squad for the World Cup finals starting in Brazil in two weeks despite a series of niggling muscle injuries which disrupted the end of his season.
Spanish media have reported that Chelsea are also poised to sign Atletico's Brazilian left back Filipe Luis and their Portuguese midfielder Tiago, who had a stint at Chelsea a decade ago.
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