Like Alvarez, Aguero played for Atletico and Manchester City.
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Alvarez is now being linked with Barcelona, but Aguero insists: "What Julián has done is extraordinary.
"He's a player capable of moving all over the pitch, with enormous sacrifice and talent. Atletico should be happy with him, as should the fans.
"I wouldn't worry about transfer rumours: this is the time to appreciate what he's bringing to the team."
Alvarez, meanwhile, said on Monday ahead of tonight's Champions League tie with Arsenal: "We're in a good moment, but we need to be more effective away from home.
"We need to improve our defense to avoid conceding goals and then be precise in attack to win games."
