The same paper had earlier claimed that Jose Mourinho’s side were considering a move for the defender, who was a huge success while on loan with Southampton last season.
Ronald Koeman’s side have an option to buy the player for around £7million, according to the report, but Madrid can pay £1.5million to remove that clause from the deal, and then look to sell him for more than that original figure to another bidder.
Mourinho is likely to be looking for another defender having relied heavily on John Terry this season, who played every minute of every game in an impressive campaign, but is not getting any younger.
Elsewhere, Gary Cahill is a regular starter but after him they only have youngster Kurt Zouma, who despite solid displays is not yet ready for a full starting place. That would make a move for Alderweireld a sensible one, given his Premier League experience this year.
The Blues also have a strong relationship with Diego Simeone’s side, having bought both Diego Costa and Filipe Luis from Atletico last summer and loaned Thibaut Courtois to them in the past.
There is every possibility that the left-back, in particular, could be used as a makeweight in any potential deal, given he has so far failed to settle in England.