The 21-year-old made his United debut towards the end of last season and has impressed in his 14 appearances in all competitions this term.
Mourinho has hailed McTominay - who is eligible for both England and Scotland - in the past and believes that he deserves more credit, as well as international recognition.
"Honestly, I think Scott deserves more than what he is getting," Mourinho told MUTV after Saturday's 2-0 win at Huddersfield Town in the FA Cup fifth round.
"I think maybe it's because he's this kind of kid profile - a normal haircut, no tattoos, no big cars, no big watches, humble kid, arrive in the club when he was nine or 10.
"He has now played already, I don't know, seven or eight 90 minutes - he's not played five or 10 minutes - in every competition: Champions League, Premier League, FA Cup, Capital One Cup.
"I think the kid deserves a little bit more [recognition]. And because it looks like England is missing him, if I was Alex McLeish the first thing I would do would be to (makes phone gesture) come to me."
McTominay, who has been with United since the age of five, has not represented England or Scotland at youth level.