Speculation has been growing in Spain that Brazil right-back Alves could be on his way out of the club after four years at the Nou Camp, most notably to super-rich Russian club Anzhi Makhachkala.
However, Alves recently pledged his future to Barca, and Zubizarreta confirmed that the player would not be leaving.
"Alves is our player," Zubizarreta said. "We renewed his contract a short time ago (until 2015), last year he appeared irreplaceable and in principle we have no intention of selling him.
The former Barca goalkeeper also moved to deny reports that the club had agrred a deal to bring Valencia and Spain left-back Jordi Alba to the club.
Barcelona-born Alba spent part of his time as a youth player as the club's La Masia academy and, having broken into the national team over the past year, the 23-year-old has been linked with a return to Catalonia.
"I can flatly deny that we have reached a preliminary agreement or have met with Jordi Alba," Zubizarreta said. "If there are two clubs I respect they are Athletic Bilbao and Valencia because that is where I played."