The highly-rated 21-year-old is one of football's hottest properties and continues to be linked with a switch to some of Europe's biggest clubs, including Barca, Real Madrid, Manchester City and Bayern Munich.
Rumours he could make the move to Camp Nou were fuelled last month when full-back Dani Alves, an international team-mate of Neymar, urged the striker to join the Catalan giants.
But Santos vice-president Odilio Rodrigues denied such speculation and confirmed the club had opened talks over a new contract for the youngster.
Neymar says he is content at the Brazilian side but maintains he will not rule out a move when he feels the time is right.
He told Placar: "I've said before, if I feel this is the right moment to leave, then why not? They say that I'll leave Santos, that I won't, but I have to stay calm.
"People make many false stories but I'm happy at Santos, trying to help my team the best way I can. I hope to win games again.
"(Comments that I'll leave now) are made by people that don't know about my life. If I feel it's time to leave, I'll leave. But this is something I'll decide, not somebody else. I'm doing well and happy at Santos."
He added of the Barcelona speculation: "There is no contract (with Barcelona), that's not true.
"Daniel Alves is a big friend but if I say (Lionel) Messi will join Santos, will you believe it? I thank Daniel Alves for what he said but I'm happy here."