The star all-rounder picked up a back niggle in the recently completed one-day series win over the Black Caps and has reportedly not trained since.
He also missed England's two-day warm-up against a New Zealand XI this week to prepare for the pink-ball Test in Auckland starting on March 22.
England assistant coach Paul Farbrace said Stokes should be fit to play in a second warm-up match beginning on Friday, even if he acted solely as a batsman.
But Farbrace insisted the 26-year-old was on track to feature with both bat and ball for the day-night Test at Eden Park.
"There's plenty of time next week for him to get overs and be ready for the Test match in Auckland," he told Sky Sports UK.
If he plays, it will be Stokes's first Test appearance since the nightclub fracas that forced him out of England's losing Ashes series against Australia.
He pleaded not guilty in Bristol Crown Court this week to a charge of affray, appearing via video link from New Zealand.
First Published: March 15, 2018, 11:53 AM IST