Talks over a fresh deal at the North London outfit appear to have stalled, which is believed to have attracted attention from numerous clubs.
As it stands, Alderweireld could be available for £25m in the summer of 2019 due to a release clause that will come into effect as long as a transfer is made 14 days before the end of the transfer window.
According to The Telegraph, PSG, who could be looking for a new manager at the end of the season, are keen to bolster their defensive options and the Belgian fits the bill.
The report adds that the Ligue 1 giants feel that their relationship with Tottenham will work in their favour as they have already done business, with Serge Aurier and Lucas Moura moving to Spurs in the last two transfer windows.
Manchester United and Barcelona have also been touted as potential suitors.