The Brazil superstar has been linked with Madrid ever since leaving La Liga rival Barcelona for PSG last August, goal.com reported.
PSG paid a world-record €222million to trigger Neymar's release clause but, although the forward fired the club to a domestic treble, reports have indicated he has failed to settle in Paris.
Spanish public broadcaster TVE reported on Monday that Madrid has offered PSG €310 million (£275m/$360m) to bring the Brazilian back to La Liga.
But Madrid quickly hit back at the claims with a statement that denied making any contact with PSG or Neymar over a possible blockbuster transfer.
"Given the information issued tonight by TVE on a supposed offer of Real Madrid to PSG and player Neymar, Real Madrid said that this information is outright false," the statement read.
"Real Madrid has not made any kind of offer to PSG or the player.
"Real Madrid is surprised that Spanish public television has been able to broadcast absolutely false information without anyone from this medium contacting any of the parties to check the alleged information that could easily have been denied."