Barcelona are at the front of the queue to sign the Brazil international, who swapped Camp Nou for the Parc des Princes in 2017.
However, it is unclear whether the Catalans will be able to afford the forward after completing a £107.7m deal for Antoine Griezmann this week.
Madrid president Florentino Perez still regrets his failure to sign Neymar from Santos back in 2013.
And that could spur the los Blancos into action, with PSG willing to let the 27-year-old go for the right price.
Neymar has won two Ligue 1 titles in the French capital, but a falling-out with the club's hierarchy means his future is in doubt.
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