It is understood former Celtic captain McNamara and former Rangers defender Mackinnon are on a short-list to replace Stewart Regan, who quit last week in the wake of his failed pursuit of Michael O’Neill to be the next Scotland manager.
Dempster, the Easter Road chief executive, is also in the frame along with McLeish, who is thought to have considerable support within the SFA’s Hampden headquarters. However, The Scotsman understands that no approach has been made to the 69-year-old, who would be unlikely to relish a return to such a high profile full-time role.
The news comes as acting SFA chief executive Andrew McKinlay quit to take up a new role in charge of Scottish Golf after five years working at the SFA, latterly as chief operating officer.
McNamara, who was capped 33 times and played at the France 98 World Cup, has been chief executive at York City since October 2016.
He moved from the dugout to the boardroom when he stepped down as manager and Gary Mills returned to boss the club, which now plays in National League North.
McNamara said earlier this week that he was not intending to apply for the job but discussed some of the challenges involved.
He said: “You have to have really thick skin. Stewart Regan has taken a lot of stick over the last wee bit. I have a bit of sympathy there. How much can he change? There are a lot of things we don’t know about going on behind the scenes.
“You aren’t just picking a manager. There are a lot of things to be resolved, sponsorships, organise friendlies, Project Brave, which I have my own thoughts on, the future of our game.
“There are so many things there that have to be looked at. It is sometimes difficult for one man to change it.
“I’m sure he would put his hands up and say he made mistakes. But then there is always the other side of it. How much did he want to change?
“When you are looking at it from the outside you only see so much. But having done this side of the job there is a bit of sympathy there because there is only so much you can do as one person.”
Mackinnon, who made over 100 appearances for Rangers between 1982 and 1986, has vast business experience since retiring from playing in the early 1990s and has held key positions at three Premiership clubs. He was appointed general manager of Kilmarnock in 2003 where he worked for over two years before becoming chief executive of Dundee, who he led out of administration. Latterly he was media and communications director at Hamilton Accies where he was also involved in player recruitment.
In between times, he was chief executive of the 110 Sport Group between 2008 and 2011 and was also a director of Sport Pathway that took sporting events to China and the Middle East.
Dempster already works at Easter Road with Rod Petrie, the Hibs chairman, who is due to become president of the SFA next season, replacing Alan McRae.
McLeish has already had a role in reforming the national association with the implementing of some of the key points from his report into the Scottish game.
Speaking earlier this week he clearly feels that a lot more has to be done in Scottish football.
He said: “It’s got to re-engage with the outside world, it’s got to modernise further.
“We need figureheads but the game is in desperate need of further reforms and relationships with government, relationships with fans, relationships with the game – it all needs to be looked at.
“What we’ve got to make sure is that we look further than personalities. Yes, I think Stewart Regan provided a lot of credibility for the game. He was a moderniser, he had our best interests at heart but let’s not believe for a minute that the future of Scottish football can revolve around one
person or two people. This is collective.
“It’s a period of failure when you reflect on where we are in terms of Scottish football, whether we should put it down to the personal failure of one person I think would be quite wrong.
“This is the trouble of Scotland, we obviously see a situation where Gordon Strachan didn’t qualify, he has to leave; we see a situation with Stewart Regan where there are issues around the national stadium, about the appointment of the manager, he has to move.
“OK, we reviewed the game in 2010 and I think at that time we went as far as we could in terms of the art of the possible. Now, I think we have to constantly reform the game.”