The 15 year-old should have signed for Real over two years ago as part of Robinho's move to Madrid. But the change of board saw drawn-up contracts left unsigned.
However, Neymar's agent, Wagner Ribeiro, will be in Madrid next week to close the agreement for a player who is regarded as a bigger talent than Robinho at the same age.
"It is true that we were going to sign a contract with Real Madrid, but then it was not done," admitted Ribeiro. "We committed ourselves to Madrid and I will meet with (sports director Predrag) Mijatovic in the coming days to treat the subject.
"Neymar is a great player for a young person and has great ambitions to join Real."
Real are also following another Santos prospect in 12 year-old Jean Carlos Chera.