The Sunday Times says Chelsea have made an enquiry about the Belgium star's interest in leaving Tottenham.
Alderweireld has three seasons remaining on a contract that pays a basic £49,000 per week.
But the 28-year-old could expect to double that amount at Stamford Bridge, it is claimed.
It is thought that discussions between Alderweireld and the club over a new deal have progressed poorly.
Spurs chairman Daniel Levy is refusing to increase the centre-back's salary to the club's £80,000-per-week ceiling.