The 27-year-old‘s first Scotland appearances came under McLeish after he had become a pivotal player for Mourinho at United. The ex-Scotland boss revealed how the Portuguese coach demanded he come down to get the midfielder into the national side.
"It was kind of crazy," McLeish told BBC Scotland's Sacked in the Morning podcast.
"Steve Clarke would have got him anyway I'm sure, but Jose Mourinho said 'Scott could play for Scotland and wants to play for Scotland so Alex McLeish should come down and sign him up'.
"So, I went down. It was during that 'Beast from the East' weather. I went to Edinburgh and was going to get a train to Manchester Piccadilly from York, but they decided the train would only go as far as Newcastle.
"Fortunately, I got another train to York but by then it was three in the morning and I was seriously thinking about turning back. But I thought I'd got that far so I would continue.”
Despite the difficulties, McLeish kept venturing down south which eventually would prove to be a great decision for him and Scotland.
"I got to the hotel at Piccadilly and the guy said 'you are down as a no-show'. I thought I had no room at 4am!
"But he found me one, I phoned the club in the morning and Mourinho said 'come at 12, have lunch - we will talk about Scott then get him in the room'.
"Jose was very accommodating and very adamant Scott should play for Scotland. Jose was my chief scout!
"Scott came in and said 'I've thought of nothing else other than playing for Scotland'. When I heard those words I thought 'we have a player'."
Napoli midfielder McTominay has 11 goals from 55 caps, including scoring six times in five games as Scotland qualified for Euro 2024. McLeish knew right away that he would be an important player for his side for years to come.
"He's the real deal, a sensational player - and a goalscorer," added the former Scotland and Aberdeen defender.
"When I was trying to bed him into the national team in a midfield role he was still learning from Manchester United players. He didn't have all the answers but did have the potential
"And he was a striker as a kid in the academy, so he has that knack of scoring."