0954 GMT July 21, 2018
The Spanish football federation has until later tonight to send the necessary documents, according to the LFP which runs France's Ligue 1, BBC reported.
If the deadline is missed, Neymar won't play for PSG at Guingamp on Sunday.
LFP has told BBC Sport it is "launching an official procedure with FIFA".
The Spanish football federation is yet to comment.
Brazilian Neymar, 25, has already had to miss Saturday's Ligue 1 win over Amiens.
Transfers between clubs in different countries must include FIFA's International Transfer Certificate (ITC). It is this document that the French football authorities are yet to receive.
"The Spanish federation of football has until Thursday night to send the ITC to the French federation of football, who send it back to the French professional football league, and then Neymar can play with PSG this weekend", an LFP statement said.
Neymar's move to France has been troubled since the release clause in his contract was triggered.
Spain's La Liga believes PSG is violating UEFA's Financial Fair Play (FFP) rules and Barcelona previously said the club would report the French side to European football's governing body, UEFA, for a FFP breach.
PSG believes La Liga is acting unlawfully, while the LFP said it was "surprised" and urged the Spanish federation to "abide by the FIFA rules".