The Ligue 2 giants had threatened legal action against the governing body following its demands of €200m (£168m) to stay in the principality if they won promotion this season
The nation's professional football clubs believe Claudio Ranieri's men hold an unfair advantage at present as they enjoy tax-free status in the principality and the league body, the LFP, has requested that the Ligue 2 leaders must move its headquarters to France if they gain promotion.
However, the FFF were faced with the prospect of legal action following demands of €200 million from its president Noel Graet if the club was to stay in Monaco, and the football association has now confirmed its intention to resolve the matter privately.
An statement posted on its official website reads: "In accordance with the decision of the Executive Committee of April 18, the French Football Federation has decided to organise a meeting between the Federation, the Professional Football League and Monaco.
"To prepare for this meeting between all parties concerned, a meeting was held last Friday at the request of the club, and between gentlemen [Noel Le] Graet, [club president Dmitry] Rybolovlev and in the presence of Willy de Bruyn, director of Monaco.
"Following this meeting, it was agreed that representatives of the Federation, Professional Football League and Monaco would meet in the week of May 20.
"The Federation reiterates its willingness to make every effort to find a solution that is able to reconcile all parties' interests."
Monaco are currently top of the French second-tier standings with only four rounds of fixtures left to play.