Los Blancos are expected to table an offer this summer for the Brazilian who moved to PSG from Barcelona for a world-record fee of £198million in the summer.
However, the Parisians are desperate to keep hold of Neymar as they try to win their first ever Champions League trophy.
If they achieve that feat this season then they could allow the 25-year-old to join Real Madrid.
And they have been urged to make a move for Neymar by La Liga boss Javier Tebas, who wants to see all of the best players in the world play in Spain.
“I would like Neymar to return to Spanish football yes,” he said.
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“The team doesn’t have to be the same, but here [in Spain] we have to be the best and Neymar is it.”
Meanwhile, Tebas also confirmed that controversial technology VAR will be used in the Spanish top flight from next season.
The reviewing system has been trialled in England this year and has received mixed reviews.
But La Liga will try their hand at VAR as the bid to eradicate refereeing errors continues.
“Next season there will be VAR,” he added.
“We are doing our best and we will ensure it arrives on time.
“With the VAR, some moments in the Barcelona and Alaves game, for example, would’ve changed.”