Martial was given time off to return home to Paris for the birth of his second child last week.
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However, the Frenchman failed to head back the USA for the remainder of United’s tour and risked being fined by the club as a result.
And manager Jose Mourinho believed his player should have returned to take part in the rest of United’s pre-season preparations Stateside.
“He has the baby and after the baby is born – beautiful baby, full of health, thank god,” Mourinho told MUTV.
“He should be here and he is not here.”
Martial’s absence from the tour left United without a senior central attacking option for their friendlies against AC Milan, Liverpool and Real Madrid.
United beat Milan on penalties before going on to suffer a poor 4-1 defeat against their Premier League rivals.
However, they did beat Real Madrid 2-1 in their final game on the US tour.
But Martial’s absence from the rest of the tour has once again raised questions over his future at Old Trafford.
The forward – who desperately lacks game time under Mourinho – has been repeatedly linked away from the club.
Earlier this summer his agent confirmed the player wants to exit Old Trafford.
United are reluctant to allow the forward to leave and it’s understood Mourinho will only sanction a move away if it is for the right fee.
The 22-year-old has been linked with a move to Bayern Munich in recent days with United keen to secure the services of Jerome Boateng in exchange for Martial.
Express Sport understands Chelsea and Tottenham are also keen.
It’s unclear whether Martial will feature in United’s final warm-up game against Bayern Munich before their Premier League season gets underway against Leicester a week today.