Barca reportedly came close to signing the World Cup winner 12 months ago and were expected to make a fresh approach following their Champions League failure.
The Catalan club are now rumoured to have cooled their interest and Atletico president Enrique Cerezo admitted to being entirely unclear on his star player's next destination.
"Griezmann has been with for five years and done a splendid job," Cerezo told Spanish broadcaster Onda Cero.
"We have a good relationship. Nice, trustworthy.
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"I hope wherever he goes he will be treated the same as he has been with us.
"I don't know where he's going, he didn't say. I don't have the slightest idea where he will go. I don't think anyone knows."
Asked whether Barca have initiated discussions, Cerezo replied: "No one from Barca has contacted me."
Griezmann joined Atletico from Real Sociedad in 2014 and has scored 133 goals in 257 appearances for the club across all competitions in total.
The mercurial striker has also won three major honours in the Spanish capital while finishing second in the voting for the Ballon d'Or on two occasions.