Real recently made an official statement denying a bid for the world-record transfer holder and teammate Kylian Mbappe during the negotiations of the Ronaldo sale to Juventus.
However, with PSG facing the Financial Fairplay tightrope and Los Blancos seemingly after another Galactico, it was expected that the club's President Florentino Perez would attempt to lure one of the forwards' to the Spanish capital.
But Luis Fernandez, who acts as the sporting director at Paris Saint-Germain's training centre, believes the Brazilian will remain in Ligue 1.
"Neymar has decided to stay at Paris Saint-Germain," Fernandez told Radio MARCA on Monday night.
"He wants to succeed, after not achieving much at the World Cup. I think he wants to win titles with PSG."
"He [Mbappe] will also stay," added the Frenchman. "He has said it, one hundred percent. He wants to win the Champions League with PSG. "[FFP] does not worry me.
"The important thing is that both Neymar and Mbappe want to stay at PSG."