Club 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, who left Villa a fortnight ago due to concerns over his health.
McLeish quit Villa's local rivals Birmingham 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."