The news comes after reports that Spurs are now resigned to losing the Belgium international in the summer for just £26million.
Alderweireld is under contract at the club until the end of next season after they triggered an extension clause in December.
This came at a price however as it meant Spurs will be obliged to accept any bid of £26m or more for Alderweireld in the final two weeks of this summer’s transfer window.
Since joining Spurs in 2015 Alderweireld has made more than 100 Premier League appearances, scoring five goals.
He has become one of the best defenders in the Premier League and has helped catapult the north London side into Premier League title contention.
The Red Devils have been looking for a top class centre-half for some time after being unable to find a tried and tested partnership in defence.
United are set to listen to offers for Eric Bailly and Alderweireld’s arrival could coincide with his departure.
Meanwhile, both Tottenham and United are gearing up for the draw for the Champions League quarter-final this Friday.
The teams will join Manchester City and Liverpool in the hat with and all could be pitted against one another.
From the quarter-final stage onwards teams from the same country can be drawn against each other.
Spurs home tie looks set to be held in their new £1billion stadium.
The club have have confirmed a number of their legends will take part in a test event ahead of the move.
Robbie Keane, Rafael van der Vaart, Dimitar Berbatov and Darren Anderton are all set to line up in a side to be managed by Gary Mabbutt.
The event will take place on Saturday, March 30.