Brendan Rodgers had been keen to bring the 24-year-old stopper to Anfield, and was hopeful of securing the player's signature ahead of the September 2 deadline.
But Atletico Madrid have jumped to the head of the queue, with Alderweireld - who has just one year remaining on his Ajax contract - opting for a move to La Liga over an Anfield switch.
Alderweireld has not been short of admirers this summer, with the likes of Everton, Norwich and Tottenham all linked to the Belgian international.
Ajax have accepted numerous offers for the versatile defender, with Spartak Moscow coming closest to landing the £5 million-rated star, only for Alderweireld to reject a move to Russia.
However, the lure of playing Champions League football with Atletico proved to be too good an opportunity to miss, and Alderweireld is expected to complete his move to the Spanish capital imminently, paving the way for Manchester City to tie up a deal for Martin Demichelis.
Liverpool must now turn their attentions elsewhere, as boss Rodgers continues in his search for defensive reinforcements.
Injuries to summer signing Kolo Toure and Sebastian Coates - as well as persistent rumours linking Martin Skrtel and Daniel Agger with an Anfield exit - led the Liverpool chief into stepping up his search for a new defender.
With the Reds' missing out on Alderweireld, Joleon Lescott has been touted as a possible alternative, with a reported £7.5 million bid likely to be enough to prize the England international away from the Etihad stadium.