Sky Italia, have claimed that Liverpool have offered 7million to the La Liga champions for the Belgium defender, who is currently at the World Cup in Brazil.
Alderweireld has failed to establish himself under Diego Simeone, having signed for the Spanish champions just last summer from Ajax.
The 25-year-old has made just 12 appearances for Atletico Madrid and is said to be frustrated at his lack of game time.
Liverpool boss Brendan Rodgers is keen to strengthen is leaky backline and the Italian media are stating that Alderweireld is one of Rodgers top transfer targets this summer.
Alderweireld can play anywhere across the backline and he was a transfer target for Liverpool before he signed for Atletico Madrid last summer.