Speculation surrounding the forward's future continues to grow as Spanish outlet Sport reported on Saturday that the France international has reached an agreement with the Catalan side that will see him move to Camp Nou at the end of the season.
The deal is said to include financial penalties should either side back out before it goes through, as Griezmann also being linked to teams in the Premier League.
Barca have already caused a stir with Atletico over their pursuit of Griezmann, as the Madrid club filed a complaint to FIFA to warn them off in December.
And the Catalan side have moved to calm suggestions that they have entered a secret pact with the 26-year-old.
"FC Barcelona denies reports that have appeared in recent hours in various media referring to Atletico Madrid player Antoine Griezmann, alleging links to our club," the statement read.
"FC Barcelona expresses discomfort in the face of these events and reiterates its respect for the institution of the Atletico Madrid."
Griezmann, who has scored eight goals in 24 appearances in all competitions this season, is contracted to Atleti until June 2022.
Diego Simeone's side are currently Barcelona's main challengers for the league title as they sit second in the table, although they sit a full nine points behind Ernesto Valverde's men.
Real Madrid have also been mentioned consistently as a potential destination for Griezmann, although Barcelona are now widely believed to be the frontrunners.