It was claimed over the weekend that Alvarez chose Atletico Madrid over Liverpool when deciding to leave Manchester City last summer.
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But agent Fernando Hidalgo told Erem News: "There were no official offers from Liverpool last season, and everything that was said is false.
"Last summer, there were no offers because Atlético Madrid didn't want to sell the player, so there were no negotiations."
The Argentine is tied to the Colchoneros until 2030. He's scored one goal in four games so far this season. Last year, he finished his first year in Atletico with 30 goals in 61 games.