Villa have been involved in constructive talks with the Scot over the past two days.
Meanwhile, on Thursday night, Sky Sports sources suggested the Second City rivals had agreed a compensation figure which was considerably lower than the ?5.4million figure which Blues were believed to be seeking. McLeish had two years remaining on his contract.
He quit as Birmingham boss just four days ago and Villa have not been deterred from pursuing the 52-year-old by the fierce opposition of fans or a war of words with their cross-city rivals.
Birmingham accused their neighbours of tapping McLeish up once it became apparent the former Rangers and Scotland boss was a contender for the Villa Park vacancy.
Blues were angry having said they were standing by their Carling Cup-winning manager after they were relegated from the Premier League last month.
Their threats to report Villa to the Premier League or to take out an injunction to prevent his appointment at Villa Park, however, have failed to materialise.
In the meantime Villa fans launched their own campaign to prevent McLeish's appointment, culminating in a protest at the stadium on Wednesday night.
Yet that depth of ill feeling has not swayed Villa owner Randy Lerner and his board, despite suggestions they ended their interest in another candidate, Steve McClaren, after supporter disquiet last week.
McLeish came into the Villa reckoning after Roberto Martinez opted not to leave Wigan last Friday.
What initially seemed an unlikely option became the source of intense speculation after McLeish tendered his resignation at St Andrew's on Sunday.
The whole process of appointing Gerard Houllier's successor has continually wrong-footed bookmakers with other initially backed candidates such as Mark Hughes and David Moyes proving way off the mark.
Rafael Benitez was also mentioned but apparently fell out of contention after asking for certain transfer guarantees.
Villa want McLeish to restore stability after a difficult year which began with the sudden resignation of Martin O'Neill five days before the start of last season.
His replacement Houllier made a number of PR gaffes and was involved in a relegation battle before leaving the club after a health scare.
McLeish had been in charge of Birmingham since 2007 following previous spells with Motherwell, Hibernian, Rangers and Scotland.
Source: Team Talk
Source: Team Talk