Mbappe claims PSG owe him 55 million euros (£46.5m) which the Parisians say the Frenchman had agreed to waive in August 2023.
The France captain has demanded the figure which includes his signing bonus which he was expecting to receive in February, his three final months of salary as well as an "ethical bonus" covering the period.
Lawyers representing the two parties met early on Wednesday after Mbappe, who joined Real Madrid this summer, had referred his case to the LFP's legal committee.
The league then made the proposition to mediate.
"Paris Saint-Germain is very pleased with today's two-hour hearing before the commission," PSG said.
"The club recalled that the player has made clear repeated public and private commitments that must be respected, having been afforded unprecedented benefits by the Club over seven fantastic years in Paris.
"In the light of the club's oral and documented arguments, the commission insisted on mediation between the parties, which Paris Saint-Germain has been seeking for many months.
"The commission has now invited the player to consider the mediation process," they added.
