Eyewitnesses have told the Manchester Evening News Martial turned up at Carrington at 8.56am and left at 9am on Thursday morning after he was informed training was later in the day.
United players reported for training on Monday at 12.30pm but were due in on Tuesday at 9am. United players started arriving at 11.30am.
Martial started the last two games against Nottingham Forest and Arsenal but failed to score and was substituted in both.
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The 27-year-old is likely to make way for new 72million striker Rasmus Hojlund, who could make his full United debut against Brighton at Old Trafford on Saturday.
Martial has scored 17 goals for United in the last three years and has not completed 90 minutes in a Premier League match since the home defeat to Sheffield United in January 2021.