McLeish resigned from recently-relegated rivals Birmingham by email on Sunday, prompting Blues chairman Peter Pannu to consult lawyers over the sudden departure.
Yesterday Villa issued a statement announcing its intent to speak to McLeish, describing him as a "free agent".
"The club has been reluctant to elaborate publicly on our search for a new manager and, in particular, to confirm or deny our interest in specific candidates," it said.
"This is not a new policy, indeed it is the approach that we have taken both in regard to managerial prospects, and potential player signings.
"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."
It added that "very serious" consideration had been given to local tensions before making the decision. "We would, however, like 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 for the role of Aston Villa manager."
In response to Villa's announcement, Birmingham issued a statement describing the move as a "contempt of Premier League and FA rules".
It said: "The club feel this will taint football and give the game and the footballing authorities a bad name if this is allowed to materialise. The club will do what is within its powers to prevent this and will lodge a formal complaint to the authorities tomorrow as there is now not the slightest doubt remaining about this tap up attempt.
"Birmingham City FC stresses that this conduct, if condoned, will open up flood gates and set a very bad precedent. This is also an attack against the intelligence and integrity of not only the Villa fans, but most importantly our fans who are badly let down after having just been relegated.
"It is definitely a bitter pill to swallow for all fans concerned, both here and across the city. Never have the two clubs seen such a strong unity between their rival fans and this unity is based on humility and integrity and what is right and fair."