According to renowned Spanish publication 'Marca', the Spanish giants continue to retain hope of luring the Brazilian to the Bernabeu as UEFA continue their investigation into the French side.
There is a possibility that the French champions could be forced to cash in on their star man in order to balance the books, with Real Madrid keeping their ear very much close to the ground on that front.
PSG are faced with accusations of inflating their sponsorship revenues to two or three times the level of those received by other clubs.
Whatsmore, there are also suggestions that PSG's Qatari owners have been illicitly pumping money into the club via their own sponsorship deals.
The outcome of the investigation will be announced by the end of august.
Meanwhile, 'Los Blancos' continue to stand firm in their stance that they will only spend big on the right player, with Neymar fitting the profile perfectly.
Whilst Neymar himself has committed himself to another season in the French capital, Financial Fair Play could yet have a say in the matter and open the door to a stunning Real Madrid swoop.
The UEFA Super Cup defeat to city rivals Atletico Madrid would certainly become much easier to deal with should Neymar sign on the dotted line by August 31.