The Spanish capital club are believed to be close to signing the talented forward, who would complete a move to the Santiago Bernabeu next summer
The 19-year-old sensation has reportedly signed a contract with Madrid already, with a transfer to the Santiago Bernabeu set to take place in the summer of 2012.
Both clubs are believed to be still in negotiations over the way the transfer fee will be distributed among the parties who own Neymar's economic rights.
Santos control 55 per cent of Neymar's rights, while two companies, DIS and Teisa, own 40 and five per cent, respectively.
Neymar has reportedly agreed a €6m-a-year deal to join Madrid, with the player's father entitled to 10 per cent of the transfer fee, plus 10 per cent of Santos' share of the sale.
The Brazil international has long been linked with a move to Spain, with both Madrid and Barcelona vying for his services.
He has refused to leave the Copa Libertadores holders before the end of the 2011-12 season as he wishes to play at the Club World Cup, in December, and at Santos' centenary in April.