The 53-year-old's contract finishes in June, and after seven years as head coach, he said he would take a month to consider his options.
"I’m looking forward to getting away from touring life for a while and having a think about my future," Stead said in a New Zealand Cricket statement.
"The past six to seven months has been particularly busy with relatively non-stop cricket action since September.
"I now want to evaluate my options but still feel I have coaching left in me, albeit not as Head Coach across all formats."
New Zealand wrapped up their home summer over the weekend by completing a 3-0 series sweep of Pakistan with victory in the final ODI in Mount Maunganui.
NZC said it would give Stead time to consider his future but would start advertising for a new head coach from next week.
"At the moment we haven’t any strong preference for either a split-coaching role or a sole appointment who covers all three formats, and we’re unlikely to be clearer on that until we see who's putting their name forward," NZC high-performance boss Bryan Stronach said.
Stead steered the Black Caps to the inaugural World Test Championship title in 2021 and to an unprecedented 3-0 Test series sweep of India on the subcontinent last year.
He was unable to end the team's long wait for a major white-ball trophy, though, overseeing defeats in the 2019 World Cup final in England and the 2021 T20 World Cup decider in the United Arab Emirates.
New Zealand missed out on a second Champions Trophy title last month, losing to India in the ODI tournament's final in Dubai.