Paris Saint-Germain, however, are apparently unsure how genuine Madrid's interest is. A source told ESPN FC that PSG are yet to receive an offer from Los Blancos for Neymar.
PSG are reportedly happy to sell Neymar to any club. Barcelona have also flirted with the idea of re-signing the player they sold in 2017 for a world-record €222 million.
But the Ligue 1 giants could use their amicable relationship with Madrid to send Neymar to Barcelona's rivals. Sources say PSG president Nasser Al-Khelaifi and Madrid counterpart Florentino Perez share a very good rapport.
Al-Khelaifi appeared to target Neymar in public comments in June, saying that he won't tolerate "celebrity behavior" from the club's star players.
Neymar then missed a training session at the beginning of July, forcing PSG to take punitive measures.
He traveled to China with his teammates but didn't take part in any of PSG's preseason matches. He also missed Sunday's 2-1 win over Rennes in the Trophee des Champions.