The Spanish publication claim Neymar told compatriot and Real Madrid left-back Marcelo to pass on a memo to Ronaldo about his plan.
Real Madrid are also in the running for the winger, with Florentino Perez a huge admirer of Neymar, who he almost signed before he joined Barca.
PSG sporting director Artero Henrique has also seemed to cast doubt on whether Neymar will stay at the club.
"I won't go back to PSG, [the decision] is irreversible", he's said to his family and friends.
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Neymar has enjoyed a stunning first season at PSG, scoring 28 goals and contributing 16 assists in 30 appearances in all competitions.
Madrid coach Zinedine Zidane tried to avoid questions about "a player who plays for another club" on Friday, but he did say he believed that such a price would soon be entirely possible.
Real Madrid have not signed a player of "Galactico" proportions since the acquisition of Welsh worldwide Gareth Bale in the summer of 2013 with only the arrival of James Rodriguez after the 2014 Brazil World Cup for 75 million euro coming close.
They are keen to see how the player is getting on with his recovery from injury and will also ask if he is keen to see out his PSG contract, which runs until 2022.