Earlier on Tuesday, Griezmann said he has made a decision on his future but refused to clarify where he will play next season when speaking to reporters at France's World Cup camp in Russian Federation.
"We understand there won't be easy matches at the World Cup for us", the Atletico Madrid star told French sports daily L'Equipe.
The Atletico Madrid forward was expected to announce his summer switch to the Catalan outfit during a press conference on Tuesday.
"I am very sorry, but I will not be revealing my decision today", he said.
"I know there's a lot of expectation, I know many were waiting for it, but today is not the day (to speak about my future)".
With Barcelona likely willing to pay €100m to secure Griezmann's services, Atletico will be up against a deadline to convince Griezmann to stay. The deal, should he sign, will make him the club's highest paid player; and the entire club has been endorsing the deal since it was offered - from the president right down to the kit man.
Griezmann is contracted at Atletico - the club he joined in 2014 - until 2022, but Barcelona are reportedly prepared to trigger his €100million release clause.