A knee injury has ruled tidy allrounder Imad Wasim out of the tour, while opener Ahmed Shehzad has been dumped.
Ali was rested for the Sri Lanka series, but is now fully fit after recovering from a knee problem, Inzamam added. He is making a comeback after gaining full fitness.
Former captain Ali was part of Pakistan's Champions Trophy-winning team in June.
Pakistan will face the Black Caps in five ODIs, starting on January 6, before a three-match Twenty20 series - for which a separate squad will be announced.
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Pakistan lost both the ODI (2-0) and T20I (2-1) series when they visited New Zealand during the 2015-16 season.
He admits that facing New Zealand in their own den would be a tough ask but also hoped that the team does well on the tour. The Kiwis always perform well on home ground, but ours is a decent unit and our performances in the last six months are there for all to see. "Even during our last tour we nearly managed to win two matches there", he said while speaking to DAWN on Sunday.
"Being a senior player, I will try to deliver what's expected from me and will contribute to the team's success", he said.
"We have been doing good in limited over Cricket and I have no doubt that team will win the series in Sri Lanka as well", Hafeez said. "I am feeling well after the rehabilitation process", he confirmed after being sidelined for injury for quite some time.
Azhar also seemed to back veteran pacer Mohammad Asif for a comeback to the national fold, saying: "Asif has a lot of experience".