The Brazilians have reached an agreement with two clubs, believed to be Barcelona and Real Madrid, and are now awaiting the player's decision on which is best for him
The two clubs to have had their bids accepted are widely reported to be Barcelona and Real Madrid.
"Santos FC announces that it has received two proposals for Neymar," said the club via its official Twitter account. "The management committee of the club decided to negotiate the [sale of the] player.
"Neymar and his father are expected in Belmiro to choose which proposal the player will accept."
The two-time South American Player of the Year, whose contract is set to expire in 2014, informed the club earlier in May of his desire to join Tito Vilanova's side.
This year's Spanish champions had seen two previous bids rejected by the Brazilian outfit but are now one step closer to sealing a deal for the Brazil international, while they also possess a secret weapon in Dani Alves, as Goal exclusively revealed in January.
Big-spending Paris Saint-Germain and their newly promoted Ligue 1 counterparts, Monaco, have also been linked to the young forward, who has already scored over 100 senior goals in Brazil, while Premier League heavyweights Manchester City and Chelsea have also shown huge interest in the prodigy.
And Champions League finalists Bayern Munich were rumoured to have wrapped up a deal for Neymar after revelations in mid-May.
As Goal revealed, Neymar was turned off by interest from Real Madrid due to the arrogant attitude of president Florentino Perez and is unlikely to make the switch to Los Blancos as a result.
The 21-year-old had previously said he intended to stay in Brazil until after World Cup 2014.