Club owner Randy Lerner held positive and productive discussions with the Scot earlier on Wednesday, according to sources close to Villa.
Lerner has identified McLeish as a prime candidate to replace Gerard Houllier, who left Villa at the start of the month.
McLeish quit Villa's local rivals Birmingham on Sunday and has flown back from a family holiday in Corsica to speak with Lerner.
Villa believe they are entitled to talk to McLeish as to their mind he is a "free agent".
The stance taken by Birmingham is somewhat different, and they are still hoping to obtain ?5.4million in compensation for the remaining two years of McLeish's contract.
The League Managers Association have criticised City for their treatment of McLeish regarding certain transfers and the sacking of chief scout Paul Montgomery.
Some sections of Villa fans have voiced their opposition to McLeish taking charge because of his association with their local rivals.
A spray-painted message reading, 'Bluenose scum not welcome' was this morning removed from the wall outside Villa's Bodymoor Heath training ground.
A gathering of angered supporters then turned up outside Villa Park this evening to protest against Lerner's plans to install McLeish.
Lerner has noted the success McLeish brought to Birmingham during the past three years, despite them being relegated from the Barclays Premier League last month.
He guided Birmingham to promotion in his first full season, secured a highest-ever top division placing - ninth - in 2009/10, and then led the team to Carling Cup glory at Wembley in February, the club's first major trophy for nearly 50 years.
Former Villa boss Ron Atkinson believes McLeish could win over supporters with a couple of major signings and by keeping hold of reported Liverpool target Stewart Downing.
Atkinson said: "You've got to admire Alex's courage for wanting it and for taking it on. But now he has to meet the hostility head on.
"He can't be a shrinking violet. He has to get out there and meet the Villa fans and tell them why he he has come to the job.
"Ashley Young is off to Manchester United but he could win favour by saying that no-one else leaves and he'll have to say 'you're not going' to Stewart Downing.
"Also nothing wins fans over more than a couple of bold, exciting signings. That will do wonders for his standing."
Source: Team Talk
Source: Team Talk