Costa shot to prominence at Atletico, which earned the forward a move to Stamford Bridge, but there have been suggestions that the forward is eager to return to Spain.
Cerezo told COPE:
“We have a magnificent relationship with the players who leave this club.
“He is a magnificent player but he is a Chelsea player. We will do everything possible and let’s see what Chelsea say because it does not depend on us.
“When pushed on whether the club would go all out for Costa, Cerezo said: ‘We always try to bring the best players and Diego is one of those.”
Costa started the season slowly but has returned to something approaching his best form in recent months and has scored eleven goals in the Premier League this campaign.
Scoring goals has been an issue for Atleti all season, confounded by Jackson Martinez’ failure to make an impact and his departure from the club in January.
Martinez signed for Guangzhou Evergrande for £32m in January and Simeone is hoping some of that money can be reinvested in bringing Costa home.
Costa has never properly settled in London and has remained in contact with various former team-mates telling several of them that he would like to return.
He even had a meeting with the club’s chief executive Miguel Angel Gil in the summer in Ibiza.
He would be the second player to have moved to Chelsea and then back to Atletico Madrid after full-back Filipe Luis completed the same journey last summer.