The 26-year-old has been heavily linked with a move away from Madrid this summer, with LaLiga champions Barca tracking the situation, as part of their quest to replace Robert Lewandowski at the Camp Nou.
Real Madrid have also registered their interest in the Argentinian, but a shock €150M bid for him was instantly rejected, as Atletico publicly mocked their rivals over the decision.
Los Rojiblancos had previously been confident of holding Alvarez to his contract in Madrid, with an enormous release clause also attached to their star striker, but the former Manchester City forward has now boldly told the club he wants to leave.
"I can't hide either. I try to be an honest person. I spoke with the people at the club I needed to speak with. The best thing for everyone is a transfer, and I want to fulfil my dream."
That statement sent shockwaves through the club as Atletico gear up for a summer dominated by what happens next with Alvarez.
Barcelona's ongoing financial issues mean an offer will be complicated as they cannot match the figure Atletico turned down from Real Madrid ahead of the 2026 FIFA World Cup.
A long-running saga looks inevitable, but Aguero - who scored 100+ goals for Atletico in five seasons before ending his playing career at Barca - has called for both sides to be pragmatic over the situation.
"He says he met with the club and decided a transfer is the best option. It's very difficult. When a player isn't happy, each club takes their own stance and the player ends up losing out," he told Jijantes FC.
"If he's not comfortable, the best thing is to find a solution and sell him. You're not going to have a player in a bad mood all year round."
Amid the ongoing speculation over his club future, Alvarez has endured a stalled start to the World Cup, with Lionel Messi and Lautaro Martinez starting both of Argentina's group stage wins so far in the USA.