'Los Cules' president Josep Maria Bartomeu admitted contacting Griezmann's agent during the January transfer window while Luis Suarez has also deemed the potential arrival of the Frenchman as "welcome".
However, these actions have enraged the Atletico hierarchy who publicly condemned the Catalan club.
"We are tired of Barcelona's attitude," Gil Marin declared via a statement on Tuesday night.
"That a president, a player and a director of the same club talk in the way they do about the future of a player with a contract in force and a few days away from playing a final of a European competition seems to me an absolute lack of respect towards Atletico Madrid and all its fans."
Speculation has been mounting given Griezmann's low €100million release clause but the CEO made it clear that Atletico will pursue further compensation if the move is completed during the summer.
"Our position is very clear and has been made public on numerous occasions," he continued. "At no time have we negotiated for Griezmann and we have no intention of doing so.
"Personally, I told the president of Barcelona a few months ago that the player's rights are neither for sale nor will we sell them.
"I also made him see that his inappropriate behavior was contrary to the integrity of the competition, since during the season we have been competing for the league title and Barcelona have been permanently pressuring one of the most important players in our team.
"I also told him at the time that, in the event that the player exercised his buy-out clause as a result of the pressure exercised throughout this season, Atletico will demand Barcelona appropriate compensation for their inappropriate behaviour.
"Now all is well, I hope this statement will help us to let our players enjoy this moment and prepare for a final as appropriate."