Real said Atletico rejected the offer based on the Argentine's 500 million euros release clause.
“Real Madrid CF announces that, following today’s Board of Directors meeting, it has made an offer of 150 million euros to Club Atletico de Madrid for the federative rights of the player Julian Alvarez,” the club said on its official website.
“After studying and evaluating it, Atletico de Madrid has thanked the club for the offer, made within the framework of the good relations existing between both clubs, and has rejected it, referring to the player’s release clause.”
The announcement comes a day after Florentino Perez won Real Madrid’s first contested presidential election in two decades, securing another four-year term.
In the run-up to Sunday’s vote, Perez had said he would spend 150 million euros on an unnamed player to be revealed on Tuesday, a fee that would represent a club record.
Alvarez scored 20 goals in 49 appearances for Atletico last season as they finished fourth in the table.