Messi cannot leave Barca until next summer, but he can start to negotiate a possible move with interested clubs Jan. 1.
Barca will elect a new president on Jan. 24 following the resignation of Josep Maria Bartomeu, which may affect Messi's decision on whether to stay or leave the club.
"I cannot talk about it at the moment," PSG's president Nasser Al-Khelaifi said on Thursday when asked about Messi's future.
After PSG's 3-1 win against Manchester United on Wednesday, Neymar told ESPN that he wanted to play with Messi next season.
"What I want most of all is to play with Messi again, to be able to enjoy him once again on the pitch," Neymar said.
"He can play in my place, I have no problem with that! But I want to play with him next year, for sure. We have to do it next season."
Messi, Neymar and Luis Suarez have remained close since their days together at Barcelona, and the three have a WhatsApp group where they still talk.
Messi's wage bill will be one of the stumbling blocks for PSG, as he earns €60 million a year at Barcelona, much more than Neymar's €36m a year or Kylian Mbappe's €20m a year at PSG.
Sources have told ESPN that the immediate priority for the club is securing extensions to Neymar's and Mbappe's contracts.