The Brazilian superstar is one of football's hottest properties and has been linked with a move to some of Europe's biggest clubs in recent months.
Manchester City, Bayern Munich and Real Madrid have all been credited with an interest in the 21-year-old in the past, while rumours suggested Barcelona had come to an agreement to take him to the Nou Camp.
Earlier this month Barca full-back Dani Alves, an international team-mate of Neymar, urged the striker to make the move to the Catalan giants.
Santos have always insisted the forward will remain at the club until at least after the 2014 World Cup, due to be held in Brazil.
The club have now revealed they have opened negotiations over a new extended deal for the forward, playing down the earlier comments by Alves.
"The club's managing committee has already decided, we intend to extend his [Neymar's] contract beyond 2014, we are working to make that happen," Rodrigues told UOL.
"We have already opened talks with Neymar's father, who denies there is any kind of agreement [with Barcelona] and we believe him. He said Neymar will be where he is happy.
"The news from Daniel Alves isn't anything new, Neymar is being sold every day, there is always news that he has been sold.
"They even say that Santos has received some money. It's very common, but there is no negotiation between Santos and any other club."
Brazilian legend Pele has also spoken out about Neymar's future, saying he should ignore any offers from England or Germany.
The three-time World Cup winner believes Neymar's game would be better suited to a move to Spain, with Barcelona his preferred destination.
"The problem is not the city that he goes to, it is where the best conditions for him will be,"said the 72-year-old.
"In England, Germany or Italy the game is harder. The referees are more accustomed to letting the play go on. Barcelona would be ideal for him.
"Santos do need him and for that reason I do not think he should push to leave, but when the time comes for both parties he should only join Barca."