Earlier this month, Griezmann revealed that he wanted his future resolved before the 2018 World Cup, where he will represent France.
Barcelona have been strongly linked with a £90m move for the attacker, and he had been expected to confirm his plans at a press conference on Tuesday afternoon.
The 27-year-old, however, has again refused to clear up his future, despite France starting their World Cup campaign against Australia this weekend.
"Sorry but today is not the day. I know there's a lot of expectation, but today is not the day [to speak about my future]," Griezmann told reporters at a press conference. "I have already made my decision but it is not the time to announce it."
Griezmann scored 29 times and registered 15 assists for Atletico during the 2017-18 campaign.