Spain's number two behind Iker Casillas has just turned 31 and has played for Barca since joining their academy in 1995.
"We let them know our interest in renewing his contract because he is a keeper of the highest level," Zubizarreta told Barca TV, after the first meeting between the club and his representatives to discuss his future.
"Before we could put forward any proposals or speak about anything, his representative told us that the decision had been considered and taken, that he would not continue after June 30, 2014. It's an irrevocable decision."
Barca coach Tito Vilanova told a later news conference he was surprised by the decision but supported his first choice keeper.
"Victor did not ask to leave, he just said he's not renewing his contract and we have to respect that," he said.
"There is never a good time for a player like Victor to say that he is leaving the club. I don't know what the ideal moment would be.
"As long as he carries on performing like he has done then I'll have no doubts about him continuing to play. I don't doubt his professionalism in the slightest.
"I don't think he's upset with us, but quite the opposite. Barca is a magnificent place, but we all have the right to go off and play in other places, cultures and clubs."
Valdes made his first team debut in the 2002-03 season and has worn the number one jersey since the following campaign, helping Barca win three Champions League titles and five La Liga crowns.
Valdes hinted at a news conference earlier this month that he would like to try his luck abroad.
Zubizarreta asked fans to "respect the professional decision of a player who has spent 12 years here. We are asking you to continue supporting him and to encourage him as much as you have done throughout his career.
"He is committed to this jersey until June 30, 2014 and will defend the goal with everything he has.
"Meanwhile, we shall work together to see what the next steps should be, along with him and his agent, to work together to deal with this situation that arose yesterday."
Reserve keeper Jose Manuel Pinto is 37 so Barca have a job on their hands to find a long-term replacement for Valdes, a brilliant shot stopper and talented ball player, who often starts off much of the side's patient possession football.
Valdes has won Spain's Zamora award for the fewest goals conceded in La Liga for the past four seasons in a row.
He is one of only two men to have won the award five times along with his predecessor at Barcelona Antoni Ramallets, who played in the 1950s and early 1960s.