The Belgian defender is keen on a move to Old Trafford and is among United's key targets, but they will look elsewhere if Spurs do not lower their asking price.
The Independent understands that United's bid for Alderweireld, rumoured to be in the region of £55m, falls short of Tottenham's valuation for the 29-year-old centre back.
The £75m fee that Liverpool paid Southampton for Virgil van Dijk in January has changed the notion of what a top-class defender is worth, and Tottenham are understood to want a similar fee if they are to part with Alderweireld.
United are unwilling to spend that sort of money on a defender and have told Tottenham that they will walk away from the deal unless the demands are lowered.
Mourinho sees Lenglet as a cheaper alternative to Alderweireld in a summer when he wants to make multiple signings. Could be a negotiating ploy - but there is only so much money to do the business he wants— James Robson (@JamesRobsonMEN) June 8, 2018
However, this may just be a smart piece of negotiation from United, and they must wait to see if Daniel Levy will call their bluff.
With Alderweireld refusing to sign a new contract and his current deal set for expiry next summer, Spurs will have to sell the Belgian either this summer or in January if they want to get a satisfactory sum.
The club can activate a one-year extension on Alderweireld's contract when it runs out next year, but a clause in the contract means that they will be obliged to sell for £25m from July 2019 onwards.
A hamstring injury kept Alderweireld sidelined for most of the 2017/18 season as he made just 14 Premier League appearances - but he should feature for Belgium at the World Cup this summer.