Over recent weeks, the 25-year-old has confided in those closest to him that he dreams of returning to Spain at the Santiago Bernabeu.
He is enjoying his time at Parc des Princes, with 24 goals recorded in just 23 appearances, but has made no secret of his desire to become a leading figure at Real.
The Blancos consider him to be the ideal heir to Cristiano Ronaldo, with the 32-year-old Portuguese being mentioned as a possible makeweight in a move for Neymar despite boasting countless records at the Bernabeu.
Neymar would relish taking on such a role, having harboured ambitions of representing Real since being in his early teens.
He spent 20 days on trial with the reigning La Liga champions back in 2006 , when he was just 13, and came close to securing a switch in 2013 following talks with Florentino Perez.
Barcelona eventually swooped to scupper those plans, but Real have refused to give up on a long-standing target.
Perez has remained vocal in his desire to get a deal done, with the Blancos president having urged Neymar to chase his Ballon d’Or dream with the Spanish giants .
He told reporters after seeing Ronaldo claim that particular prize for a fifth time in December 2017: “Being in Madrid would make it easier to win the Ballon d'Or.
“Real Madrid is a club which gives all you need as a big player, everyone knows that I already wanted to sign him at one point.”
Real could soon get their wish, despite Neymar being tied to a contract at PSG which is due to run until the summer of 2022.
There is no release clause in his current deal , such as the one triggered upon his exit from Camp Nou, with French football’s governing body (LFP) prohibiting such stipulations.
Any agreement with Madrid is therefore dependent on Al-Khelaifi giving the green light.
He is prepared to do that, but only if Neymar can help PSG to fulfil their ultimate ambition of claiming a Champions League triumph.
They have reached the last-32 stage of this season’s competition, where they are due to face Real, with the Ligue 1 leaders heavily fancied to mount a serious challenge for the continental crown.