Several reports have suggested that Diaz, 28, asked Liverpool to allow him to join Premier League rivals Manchester City last summer after being informed of their interest.
Liverpool, reluctant to sanction the deal, reportedly inquired about Alvarez, 25, in exchange, but Manchester City were unwilling to accept.
Alvarez ultimately joined Atletico Madrid for a reported fee of £82 million, and his agent, Fernando Hidalgo, has now confirmed that there were no official offers from Liverpool.
"There were no official offers from Liverpool to sign Julian last season, and everything that has been said in this regard is false," Hidalgo said.
He added, "Last summer, there were no offers because Atletico de Madrid didn't want to sell the player, so negotiations didn't take place."
The agent concluded by emphasizing, "The player is fully committed to Atletico Madrid."
