Messi, 33, is out of contract at Camp Nou next summer and is free to talk to other clubs from January onwards.
Neymar, who formed part of a potent front three with Messi and Luis Suarez during four years with Barca, has been constantly linked with a move back to the Camp Nou since leaving for PSG in a world record €222 million transfer in 2017.
"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 after PSG's 3-1 Champions League win against Manchester United on Wednesday when asked about the Argentine superstar joining him in Paris.
"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."
Neymar's comments will increase speculation that Messi could join him in the French capital in 2021.
However, PSG were also monitoring the situation and coach Thomas Tuchel has said that the Argentine would be "very welcome" in Paris.
Barca hope to be able to convince Messi to sign a new contract with the club, but talks over a renewal are on hold until a new president is elected on Jan. 24.
The new president's first task will be to sit down with Messi and his father and agent, Jorge, and sell him his vision for the club to convince him to stay.
Neymar and Messi could also be reunited at Barca. The Blaugrana tried to re-sign the Brazil star in 2019, but failed to strike an agreement with PSG over a fee.
Barca were considering making a renewed attempt to bring him back this year, too, until the coronavirus pandemic hit their transfer plans.
Neymar also made a brief comment about fellow South American Diego Maradona, who died at the age of 60 on Nov. 25: "Life is sometimes very complicated because people who had to be eternal leave and Diego had to be an eternal figure."