The silky centre-back – who is currently at the World Cup with his nation – only joined the La Liga champions from Ajax last summer, but his future at the Vicente Calderon is far from clear.
The form of players such as Filipe Luis, Juanfran, Diego Godin and Joao Miranda limited the 25-year-old to just 12 showings in the Spanish top tier, which is understood to have left him frustrated.
This has alerted Brendan Rodgers, who is desperate to strengthen his backline after his side’s poor defensive record saw them narrowly miss out on a first league title in 24 years last term.
Reports suggest that an official £7m offer is on the cards, and that the Reds are talking to Atleti to assess the possibility of a transfer.
Liverpool are keen to tie up a deal quickly as speculation of a swoop for Southampton’s Dejan Lovren has cooled, with Rodgers looking to get players in for a full pre-season.
Alderweireld is able to slot in all across the backline and has been praised for his composed playing style.