The Belgian defender had a £25m release clause in his contract, which expired two weeks before the end of the transfer window, but no club has made a serious offer for the 30-year-old.
Alderweirelds Spurs current contract expires in 12 months and the Belgium international is prepared to run it down, according to The Mirror, at which point the veteran will be free to leave on a free transfer.
Manchester United and Roma are two clubs who have shown particular interest in Alderweireld but neither side triggered his release clause, and the centre-back will have the possibility of deciding his own future should he refuse to sign a new contract with Spurs.
The north London club are hoping to receive a transfer fee for the Belgian rather than allowing him to leave for free, but Mauricio Pochettinos side are running out of time to cash-in on the defender.
Alderweireld signed for Spurs in 2015 and has been a permanent fixture at the heart of their back line for the past four years. The Belgian started their latest Premier League match against Aston Villa, and looks set to play his part this season, despite the uncertainty surrounding his future.