Santos did not say which clubs made the offers, but officials from Spain powerhouses Barcelona and Real Madrid had been negotiating with the Brazilian club for the past few days.
Details of the offers also were not made official, but Brazilian media is reporting that Real Madrid is willing to pay 35 million for Neymar, 7 million more than rival Barcelona. Real Madrid also reportedly offered a bigger salary.
Santos said on its official Twitter account that it "received two offers for Neymar" and accepted to "negotiate the player." It said Neymar and his dad were "going to choose which offer" to accept.
The player arrived at Santos headquarters around midnight Brazilian time to discuss the offers. It wasn't clear if a decision would be made right away.
Santos earlier this week reportedly rejected a 20 million offer made by Barcelona, saying it was too low.
The club has been trying to sell Neymar as quickly as possible because in six months the player will be allowed to sign a pre-contract with any other club, and the Brazilian team will not get anything in return.
The player officially rejected a 35 million offer from Chelsea in 2010, and a year later Santos said five European teams contacted the club to try to sign the youngster, who eventually re-signed with Santos until the 2014 World Cup, with a buyout clause of 65 million ($84 million).
Bayern Munich reportedly also was trying to sign the 21-year-old forward, who is touted as the future of Brazilian football and the main player carrying the country's hopes to win the 2014 World Cup at home.
Neymar is likely to join his new club after playing for Brazil in the Confederations Cup in June. The transfer window in Europe will only open in July.
Neymar led Santos to its greatest run since Pele stopped playing for the club in the 1970s. The youngster helped Santos win the 2010 Brazilian Cup, the 2011 Copa Libertadores and three straight Sao Paulo state championships. He is the club's leading scorer in the post-Pele era.
This week he topped the list of most marketable athletes in the world in a report published by SportsPro magazine, finishing ahead of Barcelona forward Lionel Messi and golfer Rory McIlroy. The list, produced in association with Eurosport, ranks athletes from across the world according to their marketing potential over the next three years.
Santos accepts offers for Neymar; player deciding
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