Neymar, 27, has been linked with a return to Camp Nou, two years after making a world-record €222million switch to Paris Saint-Germain.
But Vives, spokesman for the board of directors, tried to bat away questions about the superstar on Monday.
"It's something we're not going to get into. Now, he is a PSG player and we do not have to talk," he said.
"We will not say anything because we will fall into a trap."
Neymar's two seasons at PSG have been hampered by injuries, although he has won two Ligue 1 titles, a Coupe de France and a Coupe de la Ligue.
Vives refused to say whether the Brazil international, who spent four seasons at Barca, would be welcomed back.
"We don't leave the door open or closed," he said. "The facts are known. We explained them.
"He's a PSG player and from there we don't talk about Neymar or anyone. It's PSG. We will not do it here."