The 23-year-old completed a switch to Spain on transfer deadline day, with Atletico piecing together a package which enticed Ajax into a sale.
Liverpool had also been in the running to secure the Belgium international's signature, but saw their efforts knocked back.
The Reds ended up landing Mamadou Sakho and Tiago Ilori from Paris Saint-Germain and Sporting Lisbon, respectively, but Alderweireld claims the Anfield outfit looked at him before sealing late deals on Monday.
He told the Spanish press following his arrival at Atletico: "The club have been following me now for two or three weeks, and you could see they really wanted me.
"That is why I turned down approaches from other teams. Liverpool, for example, appeared in the last few days, but I had already taken my decision.
"The truth is that Atletico made a huge effort to convince me."