The Champions League winners have been heavily linked with the Brazilian.
Neymar joined PSG from Barcelona for a world record £200m fee 12 months ago.
Neymar has also made no secret of his desire to play for Real Madrid.
There were claims on Monday night that Real Madrid had bid €310m for Neymar in the knowledge that PSG needs to raise funds to meet FFP rules.
The report in Spain had also suggested that Neymar had been offered a seven-year deal and would earn around £35m-a-year at Real Madrid.
However, Madrid has forcefully denied those claims.
Real Madrid statement reads, “Given the information issued tonight by TVE on a supposed offer of Real Madrid to PSG and player Neymar, Real Madrid CF said that this information is outright false.
“Real Madrid has not made any kind of offer to PSG or the player,” the club said on its official website.
“Real Madrid is surprised that Spanish public television has been able to broadcast absolutely false information without anyone from this medium has contacted any of the parties to contrast the alleged information that could easily have been denied.”