The forward departed his team-mates and returned to France last week in order to be with his girlfriend for the birth of their child.
However, he did not rejoin the club while they finished up their overseas tour, leading to speculation over his exit.
Mourinho had criticised him last week for not returning, telling MUTV at the time: "Anthony Martial has the baby and after the baby is born - beautiful baby, full of health, thank God - he should be here and he is not here."
The manager continued to fuel fires of a possible Martial exit from the club when he told reporters following United's 2-1 victory in the International Champions Cup that he was uncertain if Martial would return to the club.
Martial has now taken to Twitter to provide and update on his situation, indicating that while his daughter is fine, his girlfriend had suffered through complications following the birth, which kept him away from the team.
The forward also noted that while his family would always come first, he would return to Manchester on Thursday.
"Thank you all for your messages. My little Swan is fine. For the mother it was more difficult but thank god she is better now," he said on Twitter.
"Sorry but my family will always come before everything... Back tomorrow in Manchester."
Merci à tous pour vos messages. Mon petit Swan va bien, pour la maman ça était plus difficile mais Grâce à Dieu elle va mieux maintenant. Desolé mais ma famille passera toujours avant Tout... Retour demain à Manchester 💪🏾— Anthony Martial (@AnthonyMartial) August 1, 2018
Martial's future with the club was already in question prior to this situation, having seen his playing time drop after Jose Mourinho took over for Louis Van Gaal following the 2015-16 season.
The forward's debut season at Old Trafford under Van Gaal saw him feature in 31 Premier League games, making 29 starts and scoring 11 goals.
While he has played in 25 and 30 league games over the past two seasons for Mourinho, he has been limited to just 18 starts in each of those campaigns, which had led Martial's agent to declare his client wished to leave the club.