"Julian is not for sale," the club said in a statement published by Marca. "There has been no offer for our player and no meeting has taken place."
Officials at the Metropolitano went further, describing weeks of speculation as a coordinated effort to unsettle the squad.
"We are tired of months of lies, half-truths, harassment of our players in mixed zones and absurd questions that form part of a pre-established campaign."
Crucially, Atletico Madrid were careful to separate Alvarez himself from the noise surrounding his future. The 26-year-old Argentine, who joined from Manchester City in a deal worth £82 million last summer, has scored 13 goals and contributed six assists in 35 appearances across all competitions this season.
"Julian has shown impeccable behaviour at all times," the club said. "He has given everything on the pitch and demonstrated maximum professionalism. We know this disruption has not been caused by him. He has always conducted himself perfectly."
Barcelona sporting director Deco has been reported to have met with Alvarez's agent Fernando Hidalgo in a Barcelona hotel, with the Catalan club eager to confirm a deal before the World Cup begins in mid-June. Barcelona have reportedly submitted an opening offer in the region of €90 million, including Ferran Torres as a makeweight. Atletico's response to that approach, according to multiple reports, was immediate and dismissive — the club will not negotiate below a figure believed to be between €150 million and €175 million, and are not interested in player-plus-cash packages.
Atletico's internal position is that no forced sale between rival clubs of this magnitude is realistic when the selling club has no desire to sell. Alvarez is contracted until 2030. His release clause is understood to be in excess of €500 million.
Atletico's statement comes as manager Diego Simeone has publicly insisted he is unconcerned, telling reporters he cannot speak to what goes on inside his striker's head, only to what he sees on the training pitch. "He is returning to the level he always was and we need him in this way," Simeone said.
Barcelona face a tightening timeline. Robert Lewandowski will leave at the end of next season and the club view Alvarez as the ideal long-term successor. Whether that desire translates into a bid that moves Atletico remains the question. For now, the answer from the Metropolitano is unambiguous.