Gil Marín told EFE that Álvarez's public call for a transfer — made after Argentina's 2-0 World Cup win over Austria — was inappropriate in both timing and content.
"I deeply regret his words. It wasn't the day to make those statements; it was a day for Messi and the Argentine national team, not for Julián," he said.
"Julián has a dream, and we Atlético fans have dreams too. It is true that he has spoken to us, but it is also true that he is fully aware of our position because we have been very clear: Atleti do not want to transfer his rights. He is a great player and we are very proud that he plays for us."
Gil Marín was considerably more combative on the subject of Barcelona.
"Barcelona are disrespecting us. They think they can walk all over us, that we are weak or stupid. But what they are really showing the world is a way of acting that defines them," he said.
"They lie to us, to the player, to the media — they even lie to their own supporters. They try to make everyone believe they can do a deal that in reality they are not capable of doing.
"This is not the first time Barcelona have acted like this, and the football world is well aware of it. Last year they did something very similar with Nico Williams and Athletic Club."
Atletico Madrid will formally lodge the FIFA complaint on the grounds that Barcelona engaged with Álvarez during the protected period of his contract — he is tied to the club until June 2030 with a €500m release clause.
The complaint follows Atlético's earlier rejection of a Barcelona offer and a succession of pointed social media posts from the club mocking their rivals.