The club responded to social media posts about an imminent Barcelona bid for Alvarez by mocking up parody posts of their own about Barcelona players.
Atletico, who insist Alvarez is not for sale and value him as high as £130m, posted images on X of Barcelona stars Lamine Yamal, Pedri and Raphinha in Atletico shirts.
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The posts also included joke bids for each player, including the offer of concert tickets, an annual subscription and bag of sunflower seeds for Yamal.
Alongside a picture of former Leeds winger Raphinha in their shirt, Atletico included the caption: "Don't believe everything you see, especially if it's related to Barca."
The club also said they had been "suffering a smear campaign".
"Finally, we want to take this opportunity to categorically deny that we have made an offer to the sporting director of FC Barcelona to join our scouting team in the Brazilian market," another post said.
"No, Atlético de Madrid would never do something like that. However, in recent months, we've been suffering a smear campaign against one of our players.
"Leaked information with ulterior motives, 'fake news,' constant disrespect, the culé (Barcelona) version of the propaganda machine inventing little stories, calls before direct matchups."
Barcelona declined to comment when approached by Sky Sports News. The Spanish FA has also been approached for comment.
