The player and his father have reiterated that he is not looking to leave this year and is happy to stay with Santos and in Brazil until after the World Cup finals next year.
However, Santos seem keen on striking a deal, having already confirmed talks with Barcelona and Real Madrid.
Neymar told Globo Esporte about his situation at Santos: "I'm happy here. I have already told you. Unless I die this game [against Corinthians on Sunday] is not my last game.
"If people are saying other things, then they know more than I do. Many people say what they want without knowing anything. But this is how things are."
Neymar's father Neymar da Silva Santos told Radio Bandeirantes: "Our position is to stay until the end of contract, and we have not heard that Santos are in negotiations to sell Neymar.
"If Santos want to then I will talk with my son to see if he really wants to go. We made some plans for Neymar to stay here until 2014. If these change we must be told beforehand.
"Barcelona are waiting for Neymar but for 2014. A project is in place to see how he will fit there. We are 'dating' so to speak but there is no concrete deal.
"They put people next to Neymar to see how he would work and Real Madrid do the same thing in the same way."
However, Santos vice-president Odilio Rodrigues continues to talk up a potential deal.
"There is nothing done. It depends on the negotiations," he said.
"We can't predict if Neymar will stay or not. In reality we hoped he stayed until 2014 but apparently it's hard due to the offers he received.
"He should stay until 2014, but it's a long transfer window and we will receive many offers. We will see if they are interesting or not.
"We have the idea of fighting to keep Neymar, but we have to convince ourselves that football is a business, it's the market laws that prevail.
"If an offer that is good for Santos comes and the player wants to go, we have to consider it."