Neymar only left Barcelona for the Ligue 1 champions last summer, for a world-record fee of £200million.
But according to reports in Spain, the Brazil superstar has already come to an agreement with Real.
The forward, according to Diario Gol, will spend another 18 months at PSG before returning to Spain.
Neymar is desperate to win the Ballon d’Or and believes he has a better chance of achieving his dream with the European champions.
Real president, Florentino Perez, hinted at a plan to sign both Neymar and his PSG teammate Kylian Mbappe earlier this week.
“Mbappe is 18 years old, let’s leave him to develop and see how far he can go,” Perez told El Partidazo de COPE.
“We have the best players. Recruit Neymar and wait for Mbappé to develop? That’s not a bad idea!”