Neymar, 27, is expected to leave PSG this close season, with a return to Barca after in leaving for Paris in 2017 mooted, while a shock switch to Real Madrid has also been rumoured.
"We'll see what happens. The classic response is that he plays for another team and that's that," Valverde told a news conference.
"All I know is that I'm the manager and I only think about the players I have. They are the ones I'll be using tomorrow.
"As it stands, I don't know what is going to happen."
Barca will reportedly include at least one player in a move for Neymar, with Philippe Coutinho and Ivan Rakitic among the names mentioned as possible makeweights in a transfer.
Valverde said he could not guarantee Rakitic's future, but believes he will be able to rely on the Croatia midfielder during the upcoming season if he remains at the club past the September 2 transfer window deadline.
"He is very important for us," he said.
"His work is there. Right now, I don't know if he will stay. I count on him as I have.
"In principle, nothing makes me think that I won't be able to count on him."
The upcoming Napoli fixture is the second time Barca have faced the Serie A side this week, having won 2-1 in Miami on Wednesday, courtesy of goals from Sergio Busquets and Rakitic.
Saturday's match is the Blaugrana's last pre-season clash before their La Liga campaign gets underway with a trip to Athletic Bilbao on August 16.
Their first home game at the Nou Camp will come against Real Betis on August 25.