The sought-after Brazilian is apparently being courted by the La Liga giants, as well as their rivals Real Madrid and Bayern Munich, who will be coached by former Barca manager Pep Guardiola from next season.
Neymar has previously stated his desire to stay in his homeland and while he has reiterated his current happiness at Santos, he has hinted that a move away would be a serious option for him to consider in the future.
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.
"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."