The Belgian has missed a large chunk of the current campaign through injury, being limited to only 10 Premier League appearances so far this season.
Alderweireld did return and play the full 90 minutes during the recent FA Cup replay win over Newport County, but he was then left out of the matchday squad altogether for the North London derby against Arsenal at the weekend.
The Guardian reports that Chelsea and Man City are both monitoring Alderweireld's situation and would be interested in making a move for the centre-back should he become available.
Chelsea are understood to be considering defensive reinforcements following questionable performances by Gary Cahill and David Luiz, whereas Man City could look to sell injury-prone captain Vincent Kompany this summer.
Spurs are likely to be reluctant to lose Alderweireld to a direct Premier League rival, however.