Rashford was only set to return to training on Sunday after playing a part in England's run to the World Cup third-place play-off match, in which they lost 2-0 to Belgium.
There has been no clear pecking order in terms of defensive options for United in recent seasons, with a plethora of centre-backs having been given lengthy stints in the starting XI and the unlikely sight of Antonio Valencia and Ashley Young making the full-back spots their own.
Yerry Mina seems to be the most possible option at the moment.
The German global has been one of the best centre-backs in the world over the past few years and has won a whole host of honours including 6 Bundesliga titles, 4 domestic cups and the Champions League during his time at the Allianz Arena.
Having rounded off their tour of the U.S. with a 2-1 victory over Real Madrid last week, United played their final preseason game against Bayern Munich in the Allianz Arena on Sunday evening.
Mourinho has been forced to operate with a thread-bare squad for much of pre-season and that predicament has not been helped by the arrival of just three new signings.
But Martial returned for Manchester United's pre-season games only to leave for the birth of his child.
Bundesliga expert Honigstein questioned whether Maguire has the quality to shine at Manchester United. Chelsea wouldn't want to do it either after what happened with Nemanja Matic. With the situation surrounding Anthony Martial's future at the club looking quite perilous, it could be an extremely busy week for Woodward and United on the transfer front.
The debacle has shades of the Ivan Perisic chase of last summer; where Jose Mourinho clearly wanted the Croatian, but Ed Woodward did not wish to bid the extra few million to convince Inter Milan to sell.
Jose Mourinho's hopes of bringing in his two main targets this summer were dealt a blow as one of them signalled his intention to remain with his club.