Neymar and Messi were together at Barcelona for four seasons between 2013 and 2017, combining to devastating effect in the Blaugrana's forward line.
Neymar left Barca in the summer of 2017, however, joining PSG in a world-record €222 million transfer.
The Brazilian has been frequently linked with a return to Barcelona since he left Camp Nou, nearly making the move on several occasions.
Meanwhile, Messi's future with Barca is in major doubt after a tumultuous summer that saw him request a move away, only to rescind that request after the club vowed he would have to battle them in court over the validity of his release clause.
But the Argentine's deal with Barcelona will expire at the end of the current season, meaning he could be in the final months of his legendary run with the Blaugrana.
Though it's not clear where a possible reunion would take place, Neymar insisted that he wants to play alongside Messi again after Wednesday's vital 3-1 Champions League win over Manchester United.
"What I want the most is to enjoy playing with him again," Neymar told ESPN after scoring a pair of goals against United.
When asked where that reunion would occur, Neymar said with a laugh: "He can play in my role, it wouldn't be a problem with me!"
He added: "For sure, next year we have to do it."
The Brazilian star scored in the sixth minute at Old Trafford and then sealed the match in second-half stoppage time as the Ligue 1 side went top of a tightly contested Group H.
PSG are on nine points, as are Man Utd and RB Leipzig, heading into the final matchday of the group next week.
But Neymar's side only need a draw against Istanbul Basaksehir on Tuesday to clinch progression to the knockout phase, which would leave United and Leipzig to fight for one remaining spot in the last 16.
"I've never seen myself knocked out of the Champion's League or playing the Europa League," Neymar said. "It never went through my head and it won't.
"With these difficulties, I managed to grow up, to take responsibility. I did not come here to play the Europa League."