Reports emerged in the Spanish press on Wednesday that both El Classico clubs were interested in signing the Brazilian, but Neymar dismissed them on social media as "fake news".
Barca head coach Ernesto Valverde refused to rule out the possibiltiy of him rejoining though, amid claims that a €222 million (£193m/$256m) fee would be required to secure the forward's signature.
"I wish Real Madrid and Barcelona the best of luck in their attempt to bring Neymar away from here," the defender sarcastically told reporters after his side's 5-0 win over Amiens.
"People know what our president is like, how he is with his people and how he loves our important players.
"So I don't see any reason why he should leave. He has even denied it on social media so I can't speak for him, you should ask him."
Thomas Tuchel was also unconcerned by the speculation and rubbished the claims when he was asked about them after the game.
"Pfft, I don't know about that," he said. "It is October!"
The German's doubts about the accuracy of the story are also backed up by Jordi Cardoner, Barca vice president.
Cardoner told SER Catalunya : "The Barcelona board has not considered the possibility of bringing back Neymar. It is a question that cannot be answered because no one has even mentioned it.
"He was the one who left, it would be different if we hadn't believed in him and now we wanted to bring him back, but that's not the case.
"If we did want to sign him then the board would have to discuss it but until now no one has talked about it."