Villa announced on Friday that the Scot is to fill their managerial vacancy despite opposition from certain sections of their support.
McLeish has taken the post less than a week after quitting Birmingham in controversial circumstances.
His future has been the subject of constant discussion following his departure from St Andrew's, with it unclear exactly where he stands.
McLeish and Villa are of the opinion that he is a free agent, allowing them to strike a deal.
Birmingham, though, are refusing to let the matter lie and have accused their neighbours of tapping up their former boss and breaching Premier League rules.
Blues believe they are owed considerable compensation following McLeish's decision to resign and take another job and have made it clear that they will continue to press on with their bid to get what they feel they deserve.
A statement released on the club's official website shortly after it was announced that McLeish is to become the new manager at Villa read: "The fact that Alex McLeish has been appointed as manager of Aston Villa does not, in any way, mean that the legal dispute is over and Birmingham City Football Club maintains its stance and shall vigorously pursue the matter.
"We are very disappointed with how the club and its fans have been treated by Mr McLeish given the way we have supported him over the years and we are still looking into whether Aston Villa's conduct has been in line with Premier League rules.
"As the club is currently enforcing its legal right with Mr McLeish the matter is in the hands of our lawyers and it is therefore not appropriate for the club to make any further comment at this stage.
"The club will continue its full efforts on recruiting a new manager and hope to make an appointment as soon as possible."
Source: Team Talk
Source: Team Talk