Scotland and England are both keen on McTominay, who was born in Lancaster to a Scottish father amid a tug-of-war over his international allegiance.
The 21-year-old has become a valuable member of Mourinho's side this season, beating star team-mate Paul Pogba to a spot in the starting XI for Wednesday's goalless draw against Sevilla in the first leg of their Champions League last-16 tie.
Speaking ahead of Sunday's visit of defending Premier League champions Chelsea, Mourinho said: "I've given him my advice but I think the advice of his parents is more important than mine.
"His own heart is more important than my advice, because mine is purely from a career point of view.
"More important than his career is his feeling, his family's feeling and also the overall situation with him.
"He's going to have a very good career independently of his international choice – if he has the choice, because maybe Scotland or England don't want to select him, which is also possible. The most important thing is for him to feel good with himself."
McTominay's recent rise is a boost for the Old Trafford outfit as they head into a crucial period.
Mourinho's side can move back into second position ahead of Liverpool with a win against Chelsea, though a loss would leave the club level on points with Antonio Conte's side.
Manchester United also face both Crystal Palace and Liverpool before the second leg of their Champions League last-16 tie with Sevilla on March 13.