Neymar joined PSG from Barcelona in the summer for a world record £200m.
But he is not happy in France and is already looking for a way out with Real Madrid prepared to break the bank to sign him.
It was thought they would have a clear run at him with the fee set to break the record again.
But French publication Le10 Sport claim Manchester United could also get involved in what would be a €500m (£444m) battle.
Le10 claim there is another club in the running for the Brazil ace and they believe it to be the Premier League giants.
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Manchester United held the transfer record in the summer of 2016 when they signed Paul Pogba from Juventus.
But the Neymar deal smashed that for six at the start of this season.
And he has delivered in France with 20 goals in 22 game for PSG.
But he has fallen out with Edinson Cavani and Unai Emery and looks set to quit – with Madrid his most likely destination.
Real Madrid players have been public with their comments on Neymar joining them and the Brazilian’s father is said to have already met Florentino Perez to discuss the deal.
But United could throw a spanner in the works if they are prepared to pay £444m – as reported by the French newspaper – with Madrid having been linked with a £355m move in the Spanish press.
Neymar looks set to take over from Lionel Messi and Cristiano Ronaldo as the No 1 player in world football having finished third in the Ballon d’Or rankings for two of the last three years.
United did show an interest before and believed they could do a deal when he was at Barcelona.
And they do want to make another marquee with links to Antoine Griezmann, Alexis Sanchez, and Gareth Bale.
But Neymar would be the biggest ace in the deck if they could get a deal over the line.
The 25-year-old is set to be the biggest commercial pull in the game over the next few years and United would be desperate to bring him if it was possible.