The saga involving Alvarez's potential move to Barcelona has been dragging on for the entire summer and recently the president of the Catalan giants, Joan Laporta, restated the club's desire to sign the forward.
However, in a fiery statement released on Thursday, the Atleti board have supported the decision from the club's management to refuse to sell to their La Liga rivals.
The statement read: "The members of Atletico de Madrid's board of directors have unanimously expressed their absolute support for the club's decision to not negotiate the transfer of Julian Alvarez to FC Barcelona.
"The members of the board of directors acknowledge that Atletico de Madrid is open to standard transfer market negotiations when conducted in a professional, ethical and respectful manner.
"We fully stand behind the club’s previously communicated position that FC Barcelona failed to meet these requirements and, as a result, there will not be any negotiation and there is zero consideration of an Alvarez transfer to Barcelona.
"Atletico de Madrid trust that our player will understand the decision and will remain focused on helping the club achieve its goals, just as he has done during the two seasons he has been defending our colours."
It is understood that Alvarez's desire is clear: to leave Atletico this summer and join Barcelona, with the Catalan club keen on the former Manchester City star's signature.
The saga led to Alvarez enduring a chorus of boos during Atletico's home draw against Villarreal when he came off the bench, before he exited down the tunnel on his own at full-time without applauding the fans along with his team-mates.
Since then, Alvarez has reportedly missed training on two consecutive days this week due to illness.
Alvarez has also been heavily linked with a move to Premier League champions Arsenal, with Atletico reportedly willing to do business with The Gunners, but it is unclear whether Alvarez himself would sanction a move.
The Spanish club are seeking a reported package worth around €150 million for the player, who has scored 49 goals in 107 appearances since joining Atletico from Man City in 2024.