The Belgian centre-back has been locked in contract talks with the north London club all year but an agreement has yet to be found.
It has led to speculation that the 29-year-old would be sold amid links to United, Chelsea and Paris St-Germain.
Mauricio Pochettino has avoided using him too much this year even after recovering from an injury that has ruled him out for much of the season.
There is no doubt that the former Southampton star is one of the best defenders in the Premier League, and had struck up a mean partnership with Jan Vertonghen.
But chairman Daniel Levy is likely to cash in on the Belgium international to avoid losing him for nothing.
His current deal expires at the end of next season but a clause in his deal allows him to leave for a cutthroat price for a fortnight if his contract is extended.
The Red Devils, keen to avoid getting into a transfer battle with another club, have stolen a march on their rivals by stumping up the cash now.
The Evening Standard have reported that a bid of £40m has been made for Alderweireld as Jose Mourinho looks to strengthen his defence.
And Spurs are happy to accept, after identifying the ideal replacement in the Eredivisie.
Ajax starlet Matthijs de Ligt has been scouted, and despite being 18, has been priced at £50m.
Meanwhile, midfielder Mousa Dembele is looking to secure a move to a Chinese club this summer.
He still has one year left on his contract, but Spurs are prepared to let him go.