Blackwell was sacked by Leeds two months ago with the club second from bottom in the Championship.
Ken Bates has since refused to enter into compensation talks with the League Managers' Association, and Blackwell believes he was fired for comments he made about the club's financial situation rather than for poor performance.
"We would have preferred to keep it out of court," said LMA chief executive John Barnwell. "But it would appear Leeds don't want to negotiate a settlement.
"Mr Bates has said Kevin Blackwell was not dismissed because of poor results but for negative comments made in the press about the club's finances, but having looked closely at this case we feel we have no option other than to put the matter in the hands of our lawyers."