Griezmann sealed a return to Atletico from Barcelona last August on an initial loan with an option to buy after spending just two years at Camp Nou.
He has struggled to recapture his best form with Atleti, however, having scored just eight goals in 35 appearances in all competitions.
Indeed, the France international is on a 14-game run without finding the net in LaLiga, which is one short of his longest goal drought in the competition.
Griezmann's 13 direct goal involvements in 2021-2022 is the fourth most among Atletico players, meanwhile, behind Luis Suarez, Joao Felix (both 15) and Angel Correa (18).
But contrary to suggestions in the Spanish press that Atleti is reluctant to purchase the 31-year-old outright, Cerezo has made clear a deal is being worked on.
"Griezmann is our player. He has a contract with Atletico Madrid and will stay here at Atletico Madrid," he said at an event on Friday.
"In my opinion, Antoine is among three or four best players in Europe."
Atletico last week announced that Suarez will depart the club at the end of the campaign.
It still has Alvaro Morata on its books, with the Spain international's two-year loan at Juventus coming to an end after Sunday's (AEST) Serie A clash with Fiorentina.
Unlike with Griezmann, Cerezo was less assertive when it came to discussing Morata's future in the Spanish capital.
"The truth is that I don't know what will happen to him," he said. "He's our player, but I don't know what will happen. I don't know if Juve will keep him or not. We don't know."
Atleti has conceded 42 goals in 37 LaLiga games this term, which is its worst record in a single campaign since 2011-2012 when Diego Simeone took over midway through.
Jan Oblak in particular has endured a difficult campaign, but Cerezo rejected suggestions that the goalkeeper could move on in the upcoming transfer window.
"There are always rumours about everything," he said. "Jan is a goalkeeper for Atletico de Madrid, and he has a contract. He may yet renew for another 10 years."