The statement came a day after Barca president Joan Laporta said the Spanish champions were interested in signing Alvarez amid speculation over the 26-year-old's future.
Alvarez, who helped Argentina win the 2022 World Cup, has come under fire from Atletico fans after reports linking him with a move to Barca. He was booed warming up and after coming on in Atletico's 2-2 home draw with Villarreal on Sunday.
During the 2026 World Cup, Alvarez said he had spoken to the Madrid club about a possible transfer to "fulfil my dream".
"Atletico de Madrid is open to standard transfer market negotiations when conducted in a professional, ethical and respectful manner," Atletico's Board of Directors said in Thursday's statement.
"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 had said on Wednesday there was a zero percent chance of selling Alvarez to Barca, adding: "This situation isn't about money, it's about dignity."
Laporta, however, said Barcelona's interest and offer for Alvarez would remain until the transfer window closes should Atletico decide to sell. He also said Barca had met the standards required in its dealings over the Argentine.
Spanish media have also linked Alvarez with a move to Premier League champions Arsenal.
Since joining Atletico from Manchester City in 2024 on a six-year contract, Alvarez has scored 49 goals and provided 17 assists in 107 appearances.
"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," Atletico said in the statement.