The Red Devils have already completed two signings this summer, with Shakhtar Donetsk midfielder Fred and Porto right-back Diogo Dalot heading to Old Trafford.
United have been heavily linked with a move for Belgium international Alderweireld, who is out of contract next summer.
And ex-Spurs midfielder Anderton says Alderweireld, 29, will link up with Jose Mourinho this summer, claiming United can offer the centre-back a huge pay rise.
â€śI think [Toby] Alderweireld will leave Tottenham this summer,â€ť Anderton toldÂ Bwin.
â€śUntil his injury he was the best defender in the Premier League so his situation is definitely a problem for the club.
â€śHeâ€™s an unbelievable player and he has formed a fantastic partnership with [Jan] Vertonghen.
â€śAlderweireld will move on this summer because he wants to be paid what the best defenders earn and Tottenham wonâ€™t do that.
â€śManchester United can afford to pay him far more money and he will massively boost their chances of winning the Premier League.â€ť
United will spend big this summer with Mourinho keen to keep up with Manchester City next season.
The Red Devils watched their arch-rivals storm to the Premier League title, with Pep Guardiola’s men breaking the 100 point barrier.