The defender has been heavily linked to a move to United, with Jose Mourinho thought to be an admirer of the 29-year-old Belgian.
However, according to football.london, while the sides were thought to have discussed a potential move last month, negotiations are no longer taking place between the two English clubs.
It had been speculated that any deal taking Alderweireld to United would need to include Anthony Martial heading in the opposite direction, however the Red Devils are not interested in letting the youngster go.
Spurs manager Mauricio Pochettino - who has been linked to the vacant Real Madrid post recently - is a fan of the 22-year-old Frenchman, who is thought to have grown frustrated at Old Trafford under Mourinho.
However, Alderweireld is still being tipped to leave Tottenham this summer following the breakdown in contract talks earlier in the season, which resulted in the 29-year-old losing his place in Pochettino's side.
Spurs were thought to have offered the Belgian a deal worth £130,000-a-week, however this offer was not received well by the player's representatives who believe Alderweireld - who is rated among the best defenders in the Premier League - should have been offered a contract closer to £200,000.
Alderweireld's season was scuppered by a serious hamstring injury in November which sidelined the centre back for much of the season, managing just three Premier League starts in 2018.