Having identified the France international striker as a top target, those at Camp Nou have set about trying to put a big-money deal in place.
Atletico have endeavoured to steer clear of transfer talk mid-season, with the club still chasing down Europa League glory.
They have, however, seen domestic rivals continue to push the issue, with Barca president Josep Maria Bartomeu admitting to having held talks with Griezmann’s representatives back in October and Luis Suarez hinting that he will soon be a team-mate of a much sought-after talent.
“That a president, player and a board member speak the way they've done about the future of a player with an existing contract and just a few days before disputing a European final, is an absolute lack of respect towards Atlético Madrid and its fans.
"Atlético de Madrid's stance is very clear and has been made public on numerous occasions. Not once have we negotiated for Griezmann nor do we have any intention to do so.
“A few months ago, I personally expressed to Barcelona's president that our player isn't for sale nor are we going to sell him.
“At the same time, I let him know that his inappropriate conduct was against the integrity of the competition, especially since we've been competing for the league title throughout the season and Barcelona have been continuously pressuring one of the most relevant players from our squad.
“I also told him in that moment, that in the chance the player exercised his right to nullify his contract due to their pressure throughout the season that Atlético de Madrid would demand Barcelona compensation for their inappropriate behaviour.
"Enough is enough. I hope this statement serves its purpose and that us Atlético fans can enjoy this moment and prepare ourselves for a final like we should."
Bartomeu revealed to RAC 1 that he had held conversations regarding a possible deal for Griezmann.
He said: "I saw Griezmann one day on holiday. We met with his agent, yes. It was in October.
"We talk with [Atleti president Enrique] Cerezo about many topics. We have a good relationship with them."
Suarez, meanwhile, told Radio Rincon when quizzed on Barca’s interest in the 27-year-old: "It makes the club proud to bring players of this quality like Antoine, like [Ousmane] Dembele and [Philippe] Coutinho came.
"He's a player who brings a huge amount, he has a lot of years playing at the highest level, always fighting. He rules up front for Atletico and that is fundamental.
"He is not coming to take the place of anyone, but with the ambition of winning important things.
"He will be welcomed."