The Blues and the Gunners, who are looking to sign a world-class forward to beef up their respective frontline, have been heavily linked with the 25-year-old, but the Atletico chief believes that he will be able to keep Costa for another season.
"I do not think Diego Costa will leave us at the end of the coming year," Cerezo told The Express.
The former Valladolid man has been rumoured to form part of a player-plus-cash swoop, with Chelsea's on-loan goalkeeper Thibaut Courtois as his counterpart, but Cerezo belied such possibility.
"Unquestionably, we do not want to sell him or use him as a bargaining chip for another player," he disclosed.
"We will never sell, but that won't stop teams coming in for our players."
Costa is suggested to have a £32million release clause, which, if met by interested clubs, will require Atletico to allow their prized-possession to hold possible transfer talks.