The 25-year-old Belgium international started just 12 games for the Rojiblancos last season following his move from Ajax.
Alderweireld has been linked with an array of Premier League clubs in the past, and the door may now be open after his father Viv, who is also the player's agent, told Het Nieuwsblad: "We have since last year been in several discussions about moving and Atletico understand that we do not think it makes sense to let Toby another year on the bench.
"He wants to play. If there is a solution, Atletico will not stop Toby. A loan move would be the best option, so we can revisit the situation next year."
Atletico won the La Liga title last season by a three-point margin over Barcelona.