Griezmann has been linked with a move back to Atletico during the current transfer window as part of a swap deal that would see Saul Niguez head the opposite way to Camp Nou.
France international Griezmann scored 94 LaLiga goals for Atleti across five seasons with the club before joining Barca two years ago when his release clause was triggered.
Cerezo recently refused to rule out a move for Griezmann, but the Atleti chief does not believe the 30-year-old returning would be widely accepted among Atleti fans.
Asked if there had been any development with regards to a move for Griezmann, Cerezo said: "You're not talking to the right person."
When further probed on the issue and asked if supporters would forgive Griezmann for joining Barcelona in the first place, Cerezo said: "I don't think so."
Griezmann endured a disappointing first campaign at Barca marred by injuries and inconsistency, though he did net 20 times across all competitions in 2020-2021 to finish as their second-highest goalscorer behind Lionel Messi.
He also impressed for France at Euro 2020, creating a team-high 10 chances across the tournament as Les Bleus suffered a shock last-16 elimination by Switzerland on penalties.
In his best season for Atleti in 2017-2018, Griezmann scored 19 times in LaLiga – 11 more than any other team-mate – and provided 13 assists, while only Koke (81) created more opportunities than his 65 that campaign.