'We never talk about other players'
Earlier on Friday, Barca president Josep Bartomeu said the club had made contact with Griezmann and that their former forward Neymar "wants to leave Paris St-Germain".
Brazil international Neymar left Barcelona for PSG in 2017 for a world record fee of 222m euros (£200m) and has been linked with a return.
Bartomeu also said he knows where 19-year-old Netherlands defender Matthijs de Ligt, strongly linked with a move away from Ajax, will be playing next season.
Barcelona have already signed De Ligt's international team-mate
Frenkie de Jong from the Dutch champions.
"The first contact with Griezmann was yesterday," said Bartomeu on Friday. "There is an interest, that's why we got together.
"We never talk about players from other teams.
"We know Neymar wants to leave PSG but we know that PSG do not want Neymar to leave.
"I said long ago I knew where De Ligt would play. I still know it and I cannot say more."