The French Football Federation (FFF) met the Ligue 2 champions with a view to settling its Professional Football League's (LFP) ruling that the the club must move their headquarters to the country's mainland by June 2014.
However, an agreement between ASM and the football association did not materalise following a round of talks, with the FFF suggesting that Monaco make a one-off payment of €200 million for the issue to be dropped, and the Rouge-et-blanc have now warned that they will put forward their case to the French court.
"This decision jeopardises the future of the club, so we have no other choice but to take [the matter to] the Council of State, which is the competent court to decide the legality of decisions taken by the LFP.
"We have jointly filed two appeals. One is the view to an annulment of the decision made on March 21. The other is immediate suspension of the judgment which will be rendered on our application for annulment.
"This should be urgently addressed and judged before the start of next season."
Monaco celebrated winning the Ligue 2 title on Friday night thanks to a 2-1 success at home over Le Mans.