His international team-mate Umtiti – who signed a five-year deal with Barca on Monday – said Griezmann would be a welcome recruit at Camp Nou.
However, the 24-year-old said he had no discussions with Griezmann about his future.
"I talk a lot with Griezmann but not about this topic. We talk about Playstation, food, everything, but not about this," Umtiti told a news conference.
"He is a great player and could help any team in the world. If he wants to come here, it would be fantastic."
Another player linked to Barca is Sevilla's French defender Clement Lenglet.
Umtiti said he liked what he saw from the 22-year-old, who has spent the past season and a half at Sevilla.
"I watch every game because football is my life and I think Lenglet is a great player," he said.
"I like how he plays and, in terms of if Barcelona will sign him or not, you have to talk to the managers, but I really like how he plays."