New Chelsea manager Antonio Conte has said the Spain international will stay put, describing him as a player of "fundamental importance" and now Cerezo has ruled out his return.
Costa is under contract at Chelsea until June 2019.
"He is a great player, who is very much loved, but he is a Chelsea player," Cerezo told reporters.
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"The issue is as it was six months ago or even a year ago, he is a Chelsea player.
"I've always said that Costa is a Chelsea player and has a contract with Chelsea. That's the end of this issue.
"The day we have a number nine we will announce it.
"We are looking for one and once we have him, we will announce it."
The 27-year-old Costa was handed a start for Conte's first match in charge, a 2-0 pre-season defeat to Rapid Vienna on Saturday.
(Reporting by Adriana Garcia; editing by Amlan Chakraborty)
