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The Brazil star scored twice to help PSG to a 3-1 win at Old Trafford, a result that puts the club in a strong position to reach the Champions League knockout stages.
Neymar joined the Ligue 1 champion from Barca for a world-record €222million fee in 2017, partly, it has been suggested, to escape the shadow of Messi at Barcelona.
The Catalan club won the treble in 2014-2015 with an attacking trident of Neymar, Messi and Luis Suarez, but it has been claimed the former Santos man left Camp Nou so he could have a better chance of winning the Ballon d'Or.
Neymar has since repeatedly been tipped to return to Spain but has made it clear he will stay in Paris until at least the end of the 2020-2021 season.
Messi failed to engineer a move away from Barca in the previous transfer window but, with his contract running out next June, it remains unclear whether he will choose to leave next year.
For his part, Neymar wants nothing more than to reunite with his old team-mate, telling ESPN on Wednesday: "What I want most is to play with Messi again.
"I want to play with him. I'll let him play in my position if he wants!
"Next year, we have to play together, for sure."
Neymar's two goals over United took him to 38 in the Champions League in his career. Since his debut in 2013, only Cristiano Ronaldo (79), Robert Lewandowski (60) and Messi (59) have scored more.
PSG's victory means they are level on nine points with United and RB Leipzig in Group H heading into matchday six next week.
A win for Thomas Tuchel's side over Istanbul Basaksehir will guarantee they progress as winners of the group.
