The 26-year-old - only recently back in the side following his involvement in a nightclub altercation last year - has been receiving treatment for a stiff back since the ODI series win over the Kiwis.
Stokes participated in a batting and bowling session during an indoor training session at Eden Park on Monday and managed to get through it "without any issues", Sky Sports News reports.
"His plan is to bowl tomorrow and on Wednesday outdoors," a spokesperson for the ECB confirmed. "If he comes through, which he is expected to, he will bowl in the Auckland Test."
The first Test gets underway in Auckland on Thursday.