Santos did not name the two clubs involved, but they are widely assumed to be Barca and Real Madrid, with a move to the Catalan club thought by many to be a foregone conclusion.
A statement on the Santos website read: "Santos FC announces that it has received two proposals for the athlete Neymar da Silva Santos Junior. Given the offers and conditions of the player's contract, the management committee of the club decided to transfer the player."
It added: "Neymar Jr and his father are expected in Belmiro to choose which proposal the athlete will accept."
Neymar's contract expires at the end of next season and some reports had suggested an agreement with Barcelona was as good as signed. But the striker insisted he would not be rushed into making a decision.
"This is an honour, the happiest moment of my life," he was quoted as saying on globoesporte.globo.com. "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."
His father Neymar da Silva Sr, who also acts as his manager, added: "Now we will go home, sit down and talk. We could not make a decision in the heat of the moment. Let's talk and see what Neymar wants."
Neymar, who has already played more than 30 games for his country, has spent his whole career at Santos, who have repeatedly fended off interest from a host of European clubs.
Barca have long been on his tail, while Chelsea's interest has been rebuffed in the past. All previous indications were that Neymar would join Barca, though he had also suggested previously that he would remain in Brazil until after next year's World Cup in the country.
Santos vice president Odilio Rodrigues said: "We did everything in our power to keep Neymar in Santos."