The Brazilian defender is expected to leave the club at the end of the 2014-15 season, while the Camp Nou chief is happy with Neymar and Lionel Messi
The Brazil international's existing deal with Barcelona is due to expire in the summer of 2015, but a number of reports suggested his contract could be automatically extended if he plays a set number of games.
However, Zubizarreta has made it clear no such clause exists, before insisting that Barcelona are happy to have the right-back at the club.
"I insist that both parties have agreed that his current contract will expire in 2015. It doesn’t include any extension clause," Zubizarreta said at a press conference.
"We are delighted to have him here with us and with the way he is performing."
The Barcelona director then went on to discuss the situation of Neymar at the club and was quick to dismiss suggestions the Catalans are unhappy with the Brazilian attacker.
"We have no problem with Neymar. There is absolutely no doubting his quality as a footballer."
Zubizarreta also had his say on Lionel Messi's performances and had nothing but praise for the Argentine.
"I admire him. He’s always playing against memories of him at his best and, despite that pressure, he’s always lived up the task."
Messi has netted two goals in as many La Liga performances so far this term.