On Thursday morning, La Liga attempted to derail the transfer by refusing to accept the €222 million payment for Neymar despite matching the release clause in his contract.
The organisation French organisation has now called on the Spanish body to "abide by the rules of FIFA and its responsibilities" and has offered full support to PSG in their attempts to finalise the transfer.
A statement issued on Thursday read: "The LFP is surprised and does not understand La Liga's refusal simply to accept the payment of the release clause of the player Neymar.
"The LFP asks La Liga to abide by the rules of FIFA and its responsibilities.
"The LFP supports Paris Saint-Germain and wishes Neymar to join the Ligue 1 championship.
"The LFP's legal services are in support and at the disposal of Paris Saint-Germain, so that the contract of Neymar can be approved as soon as possible."
La Liga president Javier Tebas warned this week that they would block PSG's attempts to sign Neymar for the full €222m fee and would take a complaint to UEFA's Financial Fair Play regulators if necessary.
"We will not accept that money from a club like PSG that, without belonging to LaLiga, want to benefit from the rights of our organisation," he told AS.
"If UEFA don't react, we will present our case immediately. We haven't done it yet because we thought that UEFA were going to take measures to ensure that Financial Fair Play is respected, and this 'financial doping' is avoided."
La Liga is believed not to have the authority to prevent Neymar's transfer if the buy-out clause is met but it is reported that the player could appeal to FIFA to grant a provisional transfer in order to allow him to make his debut for PSG against Amiens on Saturday.
PSG have not commented on the potential world-record deal but it is reported that the 25-year-old had been due in the French capital on Friday to finalise the move, having completed a medical in Porto.