Zuculini officially signed for City from Racing Club earlier this month and featured heavily in the club's pre-season tour of the US, scoring in a 4-1 win over Sporting Kansas City.
But with Yaya Toure, Fernando, Fernandinho, James Milner and fellow summer arrival Frank Lampard ahead of him in the pecking order, the 21-year-old will spend the campaign at Estadio Mestalla.
At his unveiling as a City player, Zuculini told the club's official website: "I’m very excited about the future.
"I am looking forward to the experiences which this move will bring and to improving myself as a player.
"I’m also very proud to be the fourth Argentine to sign for City. The club is very popular in Argentina because of Sergio Aguero, Pablo Zabaleta and Martin Demichelis."Zuculini made his debut for Racing in February 2010 at just 17 years of age and has represented Argentina at Under-20 level on eight occasions.