McTominay, born in Lancaster to a Glaswegian father, is eligible to play for both England and Scotland internationally but is yet to represent either at any level.
England manager Gareth Southgate and his Scottish counterpart Alex McLeish have each met with the 21-year-old this week in an attempt to persuade him to declare for their respective nations.
Mourinho called on McLeish to contact McTominay about his Scottish heritage after United’s 2-0 Premier League win over Huddersfield Town, having started the young midfielder ahead of club record signing Paul Pogba that day.
McTominay has since established himself as a fully-fledged member of United’s first team squad with mature displays against Sevilla in the Champions League knockout stages and during last Sunday’s victory over Chelsea.
McTominay’s manager, however, believes that he should concentrate on his Old Trafford career and claimed to have no knowledge of England and Scotland’s tussle for the player.
“I don't know if that is true,” Mourinho said. “I can't confirm because I have no information about that and my advice to him is not about national teams, is not about that.
“My advice is to keep the way he is - very humble, very open to learn, intelligent, and keep going in the same direction, same profile, trying to fight to have minutes with Manchester United.
“It is not easy and then national team will be just a consequence of his work at the club but I can't confirm at all that both national teams have contacted him.”
Mourinho has not been shy to praise McTominay since promoting him to the starting line-up and, if anything, has made a point to hail the 21-year-old’s performances as “fantastic”.
When asked whether he was surprised at how well McTominay had taken to regular first-team football, Mourinho said: “I think [it is a] consequence of his profile as a boy and I think people around him are the right people, I think.
“I’ve never met them, but I have to believe the kid with his attitude towards the others and towards football, I believe the parents must be really good people that pass to him the right values.
The United manager added: “The kid is very ‘feet on the ground’, he's very calm, so I think he passed some important tests not by the football point of view but the mental point of view - maturity, calm play against champions, play knockout in the Champions League, two tests by the mental approach.
“I think long way to go obviously but very feet on the ground, very stable and I hope he can keep the same image.”
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