TalkSPORT reports the Ajax full-back has attracted interest from a number of Premier League clubs - including Norwich City, as well as Tottenham and Liverpool - while Atletico have seen their initial offer rejected.
The Spanish giants are keen to sign the 24-year-old defender, who's also been linked with Russian duo Zenit St Petersburg and Spartak Moscow.
The report claims Ajax are seeking £6.4m for the Spurs and Liverpool target. The Belgium international is out of contract at the Eredivisie giants at the end of the season, and will be available on a free transfer.
But Spurs and Liverpool may have to act fast, as the report claims Atletico are plotting a second offer for Alderweireld.
He's believed to be keen to play Champions League football, something Atletico can offer following their third placed La Liga finish last season.
Liverpool and Spurs harbour hopes of finishing in the Premier League top four this season, but neither managed it last term.
But both clubs have been very active in the transfer market so far. Brendan Rodgers has brought in Iago Aspas and Luis Alberto from Celta Vigo and Sevilla respectively, while Kolo Toure has joined the Anfield club on a free transfer.
Tottenham have already spent almost £60m on the likes of Roberto Soldado, Paulinho and Etienne Capoue. But their spending looks far from over, especially if the Gareth Bale transfer goes through.
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