Villa owner Randy Lerner held two rounds of positive and productive discussions with McLeish on Wednesday after identifying the Scot as prime candidate to replace Gerard Houllier.
McLeish resigned as manager of Blues by email on Sunday and flew back from a family holiday in Corsica to speak with Lerner in London.
Villa believe they are entitled to talk to McLeish after claiming he is a free agent. But Blues are still hoping to obtain £5.4million in compensation for the remaining two years of McLeish's contract.
Several hundred Villa fans voiced their opposition to McLeish taking charge during a protest at Villa Park on Wednesday evening.
One of them, Chris Hearn, who had 'No McLeish' printed on his shirt, said "Our board has bankrupted Aston Villa's credibility. They aren't listening to us, but they'll notice when the team is playing in front of a half-empty stadium."
Another protester, Brian Johnson, said: "I'll be totally disgruntled if they appoint McLeish. The board got it wrong with Houllier so they needed to get this one right, and I don't think they have."
But Lerner has noted the success McLeish brought to Blues during the past three years, despite them being relegated from the Barclays Premier League last month.
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: PA