Spanish television channel TVE recently reported that the Spanish giants had tabled an offer in excess of the £200m that PSG paid Barcelona for the attacker in the summer of 2017.
However, Los Blancos issued a statement on Monday night branding the suggestions "completely false".
"Given the information tonight by TVE concerning a supposed offer from Real Madrid to PSG and the player Neymar, Real Madrid can confirm the information is completely false and have not made any offer to PSG or the player," read a statement from Real Madrid.
"Real Madrid is surprised that the Spanish television has broadcasted absolutely false information without anyone from the club being contacted to comment on the alleged information that could easily have been denied."
Neymar, who netted 28 goals in 30 appearances for PSG last season, was on the scoresheet in Brazil's 2-0 win over Mexico in the last-16 stage of the 2018 World Cup on Monday afternoon.