The Ligue 2 side is currently locked in confrontation with the LFP, which insists the club must relocate its headquarters from the principality to France in order to be allowed to compete in Ligue 1 next season.
The dispute arose as the nation's professional football clubs feel that Claudio Ranieri's men have an unfair advantage at present over their rivals as they enjoy tax-free status in the principality.
Monaco has now released a statement claiming that Le Graet, on behalf of both the FFF and LFP, has requested an exorbitant sum of money to be paid in order for the club to avoid having to push through their relocation.
"Monaco FC would like to put on public record a meeting that took place on Friday between the president of the club, Mr Dmitry Rybolovlev, and the president of the French Football Federation, Mr Noel Le Graet," the statement read.
"At this meeting, Mr Graet, acting on behalf of both the FFF and the LFP, demanded from Monaco a huge payment of 200 million euros in return for ending the current conflict without the club having to relocate its headquarters to France in order to remain in the French championship.
"The position of the club is very clear: ASM FC considers that such a demand is not only outrageous, but also totally unacceptable.
"ASM FC has been affiliated to the French Football Federation since 1919, and has, over a long period of time, invested significant sums into French football. The club has contributed many players to the French national team, and proudly represented French football in European competitions. It therefore does not understand the lack of recognition of this contribution from the French football authorities.
"The decision taken by the French football authorities - suddenly and without any consultation - is so clearly counter-productive, given that the project of the club will contribute to the whole of French football and have a positive impact on its development.
"ASM FC, after consultation with its legal counsel, has decided that it has no other choice but to bring a legal action in order to obtain a judicial resolution of the dispute.
"As part of this legal action, ASM FC will be seeking the annulment of the LFP’s decision of March 21 requiring the club to establish its headquarters in France, as well as a claim for damages from the LFP as compensation for financial and commercial losses suffered as a result of that decision.
"The club president has sent a letter to Mr Graet detailing the significant investment the Club has made into French football and providing a description of the damages that have been sustained as a result of the joint position of the LFP and FFF."