The 28-year-old seemed destined to join the La Liga champions after announcing he'd be leaving the Wanda Metropolitano after five years at the end of the season.
Griezmann, who will play for France against Turkey in a Euro 2020 qualifier on Saturday, made the claim in an interview with "Télematin".
Since arriving, Griezmann has won the Europa League, UEFA Super Cup and Supercopa de Espana in Madrid.
Atletico Madrid attacker Griezmann was believed to be on the verge of completing a deal to the Spanish champions, before reports emerged last month suggesting that the move had been vetoed.
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Daniel James is an "exciting" signing for Man Utd, says Ryan Giggs
James, 21, has already undergone a medical and the move will be completed once the transfer window opens next week. Manchester United have agreed a deal to sign winger Daniel James from Swansea. "I find it a surprising move".
He announced his decision to leave the club earlier in the summer despite having signed a contract extension just a year ago.
"I can only say that it will not be Miami", said the player, probably making reference to David Beckham's new Inter Miami franchise.
The Blaugrana are yet to see any real indication from Griezmann that he is prepared to commit his future to them so, given his reservations, Barcelona have already started looking elsewhere for attacking reinforcements. I don't have the slightest idea where he will go. The French International is seeking a move away from the club, with Barcelona linked for a potential move.
However, journalist Duncan Castles disagreed on the podcast, saying: "I think that's the issue, it would cost a lot of money".
"I can only say that it will not be Miami", he said.