The Premier League club said McLeish would be interviewed for the post "imminently", a move that will not go down well with many diehard Villa fans, although it added his Birmingham past would be taken into account.
McLeish quit Birmingham by e-mail after a contrasting season which ended in relegation to the second division, although they also won the League Cup to qualify for the Europa League's playoff round.
"The club understands that Alex McLeish is a free agent. We therefore intend to interview him imminently in order to make a decision regarding his candidacy to become Villa manager," said Villa in a statement.
Explaining the move, the statement added: "We would like, however, to emphasise that in deciding to interview Alex McLeish, the board has taken his tenure at our local rivals and the strong emotions associated with this very seriously.
"We are determined, still, not to allow that three-and-a-half year post to disqualify him should he be the best candidate."
Villa have been without a manager since the resignation of Frenchman Gerard Houllier through ill health on June 1.