Griezmann, 28, confirmed earlier this month he was leaving Atletico after five years with the club, with Barcelona reported to be his next destination.
In what is shaping as an exodus at Atletico, Diego Godin and Juanfran have both bid emotional farewells.
However, Cerezo said it was up to Griezmann to decide if he wanted to do likewise after announcing his intention to leave.
"Griezmann, I do not know if he wants to say goodbye or not, the truth is that I do not know," he said on Thursday.
"The farewell depends on Griezmann, who is the one who leaves. If he wants to say goodbye, he will say goodbye."
Griezmann won the Europa League, UEFA Super Cup and Supercopa de Espana during his time at Atletico.
Cerezo feels there is no chance the France international stays at the Wanda Metropolitano after his announcement earlier this month.
"It is irreversible. The only thing I tell him is that he has a lot of luck where he goes," he said.
"And, that at least they treat him as we have treated him here."