Jose Mourinho had lined up the Belgian centre-back as a possible arrival to strengthen his defence.
Spurs were keen to offload Alderweireld, who now has less than a year left on his contract, and handed Manchester United the chance to sign him.
According to Phil Brown, the host of the respected Beyond the Pitch podcast, Tottenham told United that an offer of £30m would be enough to do business.
However, United said no and vowed to return for him next summer.
“What’s the point of 56 scouts if Ed Woodward’s going to turn around and say ‘nah, I think he’s better so we’re going to keep Smalling and not sign Alderweireld’,” Brown told the Beyond the Pitch podcast.
“Alderweireld was offered to United for £30m and they still said ‘nah, we’ll come back for you next season’. I don’t understand that.”
Tottenham have the option of triggering a one-year extension on his current contract.
But it would in turn activate a £25million release clause for the final two weeks of next summer’s transfer window.
Alderweireld remains no closer to resolving his contract situation at the club.
Asked about it on international duty last month he said: “Honestly, I am absolutely not thinking about it at the moment.
“I feel good, play a lot right now and, therefore, am happy. We shall see.”
Barcelona are also said to be keen on making a move with a January bid possibly on the table.