Neymar could yet make his PSG debut at Guingamp on Sunday, the Associated Press has reported.
AP said the LFP told it on Thursday it had still not received Neymar's international transfer certificate (ITC) from its sister organisation in Spain, with the deadline for its arrival midnight on Friday at local time.
However, as PSG's game is not on Saturday Neymar could still be eligible if neither PSG nor the French Football Federation (FFF) refers the delay to FIFA after the deadline expires.
"If the French federation does not start proceedings with FIFA, we could still receive the ICT up until Saturday night," the league told AP.
French newspaper L'Equipe reported that PSG were unlikely to ask FIFA to rule on the issue because that could slow proceedings down further.
FIFA told AP it "has not been contacted by the FFF in connection with the player Neymar and the ITC procedure."
Neymar's world-record €222 million move from Barcelona went through last week and he was unveiled at the Parc des Princes before Saturday's Ligue 1 win over Amiens.
But he was unable to make his PSG debut that day because the certificate had not been received by the LFP.
Speaking on Wednesday, FFF president Noel Le Graet said: "I do not need to tell you that there are a few problems within the Spanish federation. I do not doubt that this will be quickly solved. Wolves do not eat each other, you know."
But he added: "The transfer is complete, so this should not last. The federation is in contact with our Spanish counterparts. There is no reason for this hold-up to continue."
Spanish radio station RAC1 reported that the reason for the delay was that the payment for the Neymar's buyout clause had still not cleared.
Barcelona are reported to still be waiting for it to clear and will not pass on the necessary paperwork to La Liga until then.
Asked for his views after the win over Amiens, PSG coach Unai Emery said he was not sure "Spain did everything" to ensure Neymar would be cleared to play without delay.