Promising midfielder McTominay was born in England but has declared his allegiance to Scotland after a minor tug of war between the neighbouring countries.
Former United boss Sir Alex Ferguson has been credited with a role in convincing the 21-year-old to snub the Three Lions.
But Brown, who coached Scotland from 1993 until 2001, feels Mourinho could also have exerted an influence, albeit on the tenuous basis of a conversation he had with the Portuguese while queuing for fast food over a decade ago.
"I read somewhere Sir Alex Ferguson was influential in McTominay's decision. But the most influential guy will have been Jose Mourinho," Brown told the Daily Record.
"Mourinho has a great affection for Scotland. He did his coaching badges at Largs and loved his time here.
"When he started at Chelsea I was at Derby and I met him at a reserve game – in the hamburger queue.
"I was watching the game with the Derby reserve team and I said to him, 'Don't you think you can come to England and beat Alex Ferguson.'
"Mourinho replied, 'No chance, it's not him or the Scottish I want to beat – it's the English!'
"If the boy had said to Mourinho, 'Scotland or England?', I think Mourinho would have steered him down the Scotland route as he is so well disposed to Scotland. I believe Mourinho would also be supportive of him playing for Scotland."