Blues are upset at Villa's statement in which they indicated they are to press ahead with plans to interview McLeish for their own managerial vacancy.
"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 on Wednesday as there is now not the slightest doubt remaining about this tap-up attempt.
"Birmingham City stresses that this conduct, if condoned, will open up flood gates and set a very bad precedent."
The statement adds: "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."