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.
"Neymar Jr and his father are expected in Belmiro to choose which proposal the athlete will accept."
The 21-year-old's contract expires at the end of next season and according to some reports, the player agreed a deal with Barcelona as long as a year ago.
But, according to Globosporte, Neymar will now evaluate the two offers with his family before making a decision.
A statement from the club 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 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."
Neymar, who has already played more than 30 games for his country, has spent his whole career at Santos, who have repeatedly turned down offers for the player from a host of European clubs.