Sweden reached the quarter-finals of the competition, further than many predicted them to reach and much of their good play was centered on the former Benfica man.
Yahoo add that United, who tried to sign Alderweireld before the World Cup in Russian Federation this summer, have received encouragement an agreement can be reached before this season.
Mourinho has around 17 senior players available for the tour of the United States, which will start with a flight to Los Angeles on Sunday.
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Varane has been linked with United for some time as Mourinho was the man in charge at Madrid when he joined the La Liga giants from Lens in 2011 and the Portuguese coach has reportedly been keen on a reunion since taking over at Old Trafford.
Spurs have the likes of Davinson Sanchez and Eric Dier already in the squad to compensate from a potential Alderweireld exit, which begs the question of what Tottenham should do if they are left with £60million burning in their back pocket.
As reported earlier, Croatia crushed England's dream with a 2-1 extra-time victory.
The pre-season tour in the United States could see Mourinho promote six teenagers up to first team duty in place of his men still out in Russian Federation.