Aston Villa owner Randy Lerner arrived in Kristiansund, Norway, on Thursday night to talk to Ole Gunnar Solskjaer about the vacant managerial role at Villa Park.
Solskjaer is currently overseeing his second season as coach of Molde, after he guided them to their first ever title in his debut season as a manager in 2011.
The Norwegian was reserve team manager of Manchester United for three-and-a-half-years after he ended his 11-year playing career with the club in 2007.
The 39-year-old signed for the Reds from Molde in 1996 for a bargain £1.5m and went on to win six Premier League titles, two FA Cups and scored the winner in the club's 1999 Champions League final triumph.
He was rated at 12/1 in the aftermath of McLeish's dismissal on Monday, but has now emerged as favourite ahead of Norwich City boss Paul Lambert.
The Villans sacked Alex McLeish on Monday after a dismal season in which the club won just seven Premier League matches.
Jan Aage Fjortoft tweeted on his former team-mate's future:
The Scot was an unpopular choice with supporters when he crossed the city divide from Birmingham City, after Lerner's approach for Wigan Athletic manager Roberto Martinez proved unsuccessful. The Latics finished five points and one place ahead of the Villans.
McLeish said of his dismissal: "When I accepted the role as manager of Aston Villa Football Club I was acutely aware of the responsibility I had to find the best way to serve the great traditions of one of the finest clubs in professional football.
"I was truly honoured to have been given the opportunity to manage the club, which plays such an important part in the fabric of the local community and to its worldwide fan base.
"I relished the challenge and, together with my loyal and very capable staff, dedicated all of my efforts into moulding a successful team.
"My only regret in leaving now is we weren't able to achieve more for the supporters and their high expectations.
"Finally, I want to take this moment to say that I have nothing but the highest respect for the club and sincerely wish it and the fans great success in the future."