The 29-year-old Spain international has been locked in contract negotiations with the club ever since he reportedly rejected terms offered earlier in the autumn.
Iniesta's reluctance to sign a new contract has subsequently led to heightened speculation regarding the player's future, with reported interest from the likes of Manchester United and Manchester City.
However, the midfielder himself made it clear he intends to sign a new deal following the 2-1 Clasico win over Real Madrid in October, and former goalkeeper Zubizarreta is adamant the former Uefa Best Player award winner could put pen to paper before Christmas.
"We're close [to agreeing a new contract with Iniesta], yes," Zubizaretta told Radio Catalunya.
"I think he could sign before Christmas."
Iniesta, who is currently on international duty, currently has a contract at Camp Nou until June 2015.