The Barcelona sporting director expects the 29-year-old midfielder to extend his deal sooner rather than later despite speculation he could be tempted away from the club.
The 29-year-old Spain international has been locked in contract negotiations with the club since he reportedly rejected terms offered earlier this fall.
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 Zubizarreta is adamant the former UEFA Best Player award winner could put pen to paper sooner rather than later.
"We're close [to agreeing to a new contract with Iniesta], yes," Zubizaretta told Radio Catalunya. "I think he could sign before Christmas."
Iniesta, who is on international duty, currently has a contract at Camp Nou until June 2015.