The Spanish giants are monitoring the situation closely due to the possibility of UEFA sanctions being handed down to PSG.
Los Blancos are still seeking a marquee signing to replace Cristiano Ronaldo who left the Bernabeu for Juventus this summer.
Neymar played for Real’s bitter rivals Barcelona prior to his £198m move to the Ligue 1 champions last year.
But the Brazil international has been rumored to be unhappy in the French capital almost ever since his arrival.
With two weeks left until the Spanish transfer window closes there is plenty of time for Real to attempt to bring Neymar to Madrid.
Indeed, according to Sport, Blanco’s president Florentino Perez is lining up a huge £269m bid to make the deal happen.
They temper the news, however, by reporting that such is bid is only likely to be tabled should PSG be forced to sell due to UEFA handing them a serious punishment.
The governing body are currently investigating certain sponsorship deals presented by the Parisian club.
Meanwhile, Yuri Berchiche who played alongside Neymar at PSG believes Real have a good chance of signing the 26-year-old forward should they attempt to.
“I see him returning to Spain but more in white than in blue and red,” he told El Larguero.
“He was very happy at Barcelona. He still likes La Liga because I spoke with him about it, we have a good friendship, and he’s a fantastic person.
“If he joins Madrid I wish him the best of luck.”
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