The Foxes ace is expected to replace Phil Jones or Smalling in Mourinho's starting 11, as he has done with the Three Lions.
The Daily Mail say that United will have to sell one of their current crop of centre backs in order for Mourinho to get hold of Maguire, Leonardo Bonucci or Toby Alderweireld with the Leicester City man potentially costing £65 million.
Claude Puel has considered potential replacements regardless with Barcelona's Yerry Mina and Gary Cahill both discussed.
Undermanned following the World Cup, United were disjointed and void of creativity as they fired a blank against the MLS strugglers.
Maguire, who only arrived at the King Power stadium a year ago in a £17m move from Hull City, has become one of the hottest properties in the English game after his standout performances in the World Cup and the Mail says Mourinho was mightily impressed by his "mental toughness".
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However, one major snag is that the summer transfer window is scheduled to close on August 9, when Three Lions squad members to the summer World Cup will be returning from their extended vacation.
The 22-year-old has told the Red Devils he wants this leave this summer as he looks to secure first-team football.
Though the Argentine isn't an indispensable player, it is a little unusual to hear Jose is willing to move him on since he was solid at times for the club in the season before last. Bundesliga giants Bayern Munich are also interested in Martial.
Woodward is understood to want to keep Martial and will trigger the striker's one-year extension clause, to protect United's financial investment in him, if they do not receive the fee they want.