The colossal transfer claim was made by Spain’s public television station TVE on Monday evening.
Real were quick to knock it down, saying in a statement they had not been consulted by TVE before the broadcast.
“Real Madrid have made no offer of any kind to PSG or the player,” the European champions added.
The report came hours after Neymar’s Brazil saw off Mexico 2-0 in the World Cup last 16 in Russia to set up a tantalising quarter-final clash with Belgium.
Neymar, 26, became the world’s most expensive player last year when he moved to PSG from Barcelona for 222 million euros.