Santos have accepted two offers for their star player, with Barcelona confirmed as one of the bidders and Real Madrid widely suggested to be the other side in pursuit.
After an initial meeting between club officials, Neymar and the player's father, no immediate decision on his future was reached, but Spanish media have since reported the forward will be moving to the Nou Camp.
A statement from Santos read: "In a meeting with representatives of the management committee of Santos FC, striker Neymar Jr was made aware of the offers received by the club and he will analyse them in the coming days before making a final decision."
The 21-year-old's contract expires at the end of next season and some reports had suggested an agreement with Barcelona was as good as signed.
Santos vice-president Odilio Rodrigues apparently shares that view, quoted on the website of Spanish sports newspaper Diario AS as saying: "When I went to Barcelona to hear the offer, I learned that Neymar had a verbal agreement that when he finished his contract in 2014 he was going to Barcelona.
"He has a gentleman's agreement. He doesn't have a contract, but a verbal agreement."
The move to Barcelona was reported as a done deal by Marca.com, the website of the sports newspaper that most closely focuses on affairs at Real Madrid.
If Madrid are to miss out on Neymar, they will have to work out a way to contain him during the 'Clasico' matches next season.
Barcelona assistant boss Jordi Roura refused to be be drawn on the progress of Barcelona's chase, but acknowledged the talent of their target.
"Let things run their course," he said. "He's a spectacular player and any club would want him."
It was reported by Marca.com that Neymar's signing could be announced after Barcelona's Primera Division match at Espanyol on Sunday night, or during Monday.
Neymar, who trained with Santos on Saturday, is relishing the prospect of a move to Europe, being quoted by Brazilian sports website globoesporte.globo.com as saying last night: "This is an honour, the happiest moment of my life. I will now think carefully about these two proposals.
"I will decide with my family. I'm in no hurry. The decision may come out in five minutes, half an hour or three days."
Neymar, who has already played more than 30 games for his country, has spent his whole career so far at Santos, who have repeatedly fended off interest from a host of European clubs.
The club initially confirmed two bids had been accepted with a statement which read: "Santos FC announces that it has received two offers for the player Neymar da Silva Santos Junior.
"Given the offers and conditions of the player's contract, the management committee of the club have decided to sell the player."
It remains to be seen whether the transfer will be complicated by the complex nature of Neymar's ownership arrangement, with various investment groups holding a stake in the player as well as the club.