Griezmann, 27, has been linked with a move to Barcelona after enjoying another fine season with Atletico, scoring 27 goals in all competitions and helping his club reach the Europa League final.
Suarez strongly suggested the France international, who is contracted until mid-2022, would be making the move to Camp Nou.
"It makes the club proud to bring players of this quality like Antoine, like [Ousmane] Dembele and [Philippe] Coutinho came," he told Radio Rincon .
"He's a player who brings a huge amount, he has a lot of years playing at the highest level, always fighting. He rules up front for Atletico and that is fundamental.
"He is not coming to take the place of anyone, but with the ambition of winning important things.
"He will be welcomed."