Recently breaking into the United team, McTominay was wanted by both countries as part of their national team squads.
However, he made the decision to go with Scotland, and Brown believes Mourinho was a part of that decision.
"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.
"It's a massive coup for Alex [McLeish] to land McTominay for Scotland. Pipping England to get a player is just like beating them in a game."