The Brazilian forward did not answer questions about his links to PSG at a sponsorship event in Miami on Friday, although he has featured for Barca in their pre-season matches.
Former captain of the Catalan giants Puyol believes it is time Neymar, who stormed out of a training session following a bust-up with Nelson Semedo, spoke up about his intentions amid talk of a €222million switch to France.
"I do not know what's going to happen," Puyol told Marca. "He's the one who has to talk and explain what he wants to do, because I cannot control him.
"The decision should be taken by him. I am not responsible for the club so I do not know if they have decided something.
"I do not know if he has dreams of leaving, but it's harder for a player to do stay with the same team for their whole career. Football is changing but there are still cases: [Lionel] Messi, [Sergio] Busquets, [Andres] Iniesta. I think he has love for the shirt but then there are other factors."
Puyol said he thinks the new Barca coach Ernesto Valverde will stay true to the club's values after he succeeded Luis Enrique at Camp Nou.
"Luis Enrique did a great job, he won a lot of titles with a great team," the former captain added. "Now another coach comes in.
"The football ideals of the club will not change. It will have its nuances, as with every coach, but the idea is the same. His teams have worked very well. Let's see how he is doing. He has a spectacular squad, I am sure he will be fighting for all the titles."