This week the authority disqualified Massimo Cellino from owning a club as he failed its Owners' and Directors' Test. The Italian could be forced to sell the club he bought earlier this year, but the club say they are taking legal advice and Cellino says he will appeal the ruling.
The petitions claim that Cellino has brought stability to the club, and forcing his removal would cause more harm than good.
The Football League called on the Italian to resign immediately saying he could not own the club until after 18 March 2015, when a conviction is spent under UK law.
The club's supporters' trust has called for stability at Elland Road and clarity from the Football League after a tumultuous period under Cellino.
The Football League has not yet responded to requests for comment on the petitions.