Sky Sports News understands United have approached Leicester to sign Harry Maguire while fellow centre-backs Yerry Mina and Toby Alderweireld are understood to be other options.
United continue their International Champions Cup (ICC) campaign against Real Madrid in Miami on Wednesday (01:05 BST), before facing Bayern Munich in a friendly at the Allianz Arena the following Sunday (19:15 BST).
Diogo Dalot, the £19 million (S$34 million) summer signing from Porto, is out until September with a knee issue and Marcos Rojo is back at Carrington for treatment on an injury he suffered at the World Cup with Argentina.
Mourinho is still without a number of players, who reached the latter stages in Russian Federation, and made clear his preference that they cut their breaks early to aid preparations for the season opener against Leicester on August 10.
"I think the passion many Americans have for soccer deserves more".
Following the defeat, Manchester United coach Jose Mourinho expressed his concern with the club's youth team.
"The negativity is just one of an array of factors that Manchester United fans are not happy with - and that despondency has crept into punters thoughts ahead of the 18/19 season".
"I don't know", Mourinho replied when asked when Matic would return.
"We are not playing here to improve the team, the dynamic or our routines". Star players like Paul Pogba, Romelu Lukaku and Ashley Young are still absent following the World Cup.
'I would like two more players.
Speaking about Valencia, Mourinho told MUTV: "Antonio came from holiday, I think too much holiday for him, his condition was not good when he was back". Alexis is the only attacking player that we have.
"Joe Gomez, playing in that role as a central defender, he combines a lot of things you don't find on the transfer market so I don't see the need at the moment".
"That's not normal after four days in the club - adapting that well to the style of play,"he said after the game".
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