Alderwiereld was left out of the side who drew 2-2 with Juventus in the Champions League on Tuesday - despite claiming that he had fully recovered from a hamstring injury and was fit to play.
Chelsea, Manchester City and Manchester United are also interested in the defender as speculation about his future continues to mount. The Argentine signed a new five-year deal in 2016 worth £5.5m a year.
Tottenham star Toby Alderweireld is being eyed up for a transfer swoop by Real Madrid and Chelsea after he found himself snubbed from the club's Champions League clash against Juventus, according to a report.
Tottenham have been in talks with Alderweireld about a new deal for the Belgium worldwide, but Spurs' wage cap is proving to be a stumbling block.
Although the Portuguese manager bought in Eric Bailly and Victor Lindelof, Toby Alderweireld represents a more experienced option. The Belgian appears destined to leave Manchester United when his contract expires at the end of the season, despite Jose Mourinho's best efforts to keep him.
Manchester United midfielder Marouane Fellaini has agreed a deal to join Besiktas at the end of the season.
Spurs midfielder Erik Lamela is open to leaving the north London club for Inter Milan.
Arsenal and Chelsea are keeping close tabs on the progress of Luke Shaw's contract talks with Manchester United, reports the Mirror.
Real Madrid are planning to spend around 600m euros (£534m) on improving their squad this summer, with Tottenham's 24-year-old England striker Harry Kane a key target.
Alderweireld is now contracted at Spurs until the summer of 2019, which could be extend to 2020 due to a one-year extension option.