Real Madrid have dismissed as "absolutely untrue" reports of a 310 million-euro ($360-million) bid for Paris Saint-Germain's Neymar that sparked rumours he could serve as a replacement if superstar Cristiano Ronaldo leaves the Spanish giants.

The colossal transfer claim, which would dwarf the 222 million-dollar deal that made Neymar the world's most expensive player last year, 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," added the European champions, the home of Ronaldo since 2009.

TVE stood by its reporting however, saying on its website that the claim came from sources it considered to be the "most reliable".

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.

Despite Real's strong rejection, the transfer rumour mill swirled at the possibility of a galactico swap, following hints that both Neymar and Ronaldo could be unhappy at their star-studded clubs.

Neymar, 26, moved to PSG last year and went on to score 19 goals in just 20 league games before suffering a foot injury in February that required surgery in Brazil.

He only returned to France in May, fuelling speculation that he could seek to leave the club after just one season.

Ronaldo, who had shined in the World Cup before his Portugal side was beaten by Uruguay on Saturday, cast doubt over his commitment to Real after winning the Champions League in May.

"It was very nice to be in Madrid," he said, adding that "in the next few days I will give an answer to the fans".

He later walked back the statement, but doubts over his future at Madrid have lingered.

Real Madrid has also been thrown into flux after coach Zinedine Zidane stepped down in June having steering the club to a third successive Champions League trophy.

His replacement Julen Lopetegui said in June that Ronaldo is a player he wants "at his side always".