Cellino was due to begin a 12-month suspension on February 18 after the FA found him guilty of breaking its agency regulations in relation to the 2014 sale of Ross McCormack to Fulham.
The Italian immediately declared his intention to appeal against the verdict, which was handed out on December 8, and succeeded in getting a six-month reduction.
However he maintains his innocence and is now appealing against the decision for a second time, using the FA's 'Rule K'.
In a statement, the club said: "Mr Cellino alleges the decision of the FA Appeal Board was irrational, procedurally unfair, and that there was apparent bias.
"All other aspects of the arbitration shall remain confidential until such time as a decision has been made. Once a decision has been reached by the Tribunal it will be published."
Last month Cellino sold half of his stake in Leeds to fellow Italian Andrea Radrizzani. Leeds currently sit fifth in the Sky Bet Championship.