Alderweireld joined Spurs from Atletico Madrid in the summer of 2015 after an impressive loan spell with Southampton during the 2014-15 campaign.
The former Ajax youngster has been one of the most consistent centre-backs in the Premier League over the last couple of years, but injuries have restricted him to just 10 Premier League appearances this term.
Alderweireld's deal with Tottenham will expire at the end of next season, and it is understood that Spurs have decided to pull the plug on contract talks as they are not willing to meet Alderweireld's 'excessive wage demands', which are believed to stand at £180,000 a week.
United and PSG have both been credited with an interest, but according to The Mirror, Chelsea have now joined the race as the Blues look to boost their defence in this summer's transfer window.
Alderweireld could be available for £25m next summer due to a release clause that will come into effect as long as a transfer is made 14 days before the end of the window.