The Brazil international is in the final year of his contract and has been linked with the likes of Paris Saint-Germain, Inter and Liverpool throughout the close-season.
New Barca head coach Luis Enrique stated last month that the former Sevilla man was committed to Camp Nou.
And Zubizarreta confirmed there was no update on the status of the 31-year-old.
"Dani Alves has a contract with Barca," he said at a press conference presenting Thomas Vermaelen as a Barcelona player. "At no point have we spoken about him leaving.
"He came back after his holidays and trained with the club. That's how it is. We have had no information from his agent or that type of thing that something might happen.
"Things can chance, this is football. But we have no offers for Dani Alves so we're working with him as a player in our squad. He's training very well."
Zubizarreta was also asked about the possibility of signing Fiorentina winger Juan Cuadrado, but would refuse to be drawn on rumours that a deal was imminent.
"I never talk about signings or names before they happen," he added.
"I'm not going to enter into that debate. We always work here on improving the squad to provide greater options to the coach and that's what we're working on."