But the England captain was shut out for the third game in a row as Belgium sealed a 2-0 win in the third-place play-off.
Tottenham could activate a clause in Alderweireld's current contract that would ensure the 29-year-old remains at White Hart Lane until 2020.
United boss Mourinho is desperate to sign a centre-back this summer to bolster his defence.
Spurs believe the defender is valued at the same price as Virgil van Dijk was which was around £75m while Jose Mourinho is said to be unwilling to part with that much money.
Despite his lack of club football, Alderweireld enjoyed an impressive World Cup campaign in Russian Federation, starting and completing all of Belgium's matches bar their dead rubber group contest against England where a host of first-teamers were rested.
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Alderweireld's 2017-18 campaign was largely disrupted by a hamstring injury which initially ruled him out of action for four months, with a recurrence of that problem further delaying his return.
Alderweireld started just three Premier League matches in 2018.
Toby Alderweireld has claimed that his omission from the Tottenham Hotspur team in the second half of last season was "unjustified".
Pavard hit the headlines during the World Cup thanks to that remarkable goal against Argentina which many are picking as the best of the entire tournament and that quality clearly hasn't gone unnoticed.
'I wanted to prove something to me, show that the period before the tournament in which I - for whatever reason - did not play, it was unjustified.
"I wanted to show that I am still the same Toby as in November".More news: Cave diver considers suing Elon Musk for calling him a 'pedo'