The twilight match will be played at Auckland's Eden Park, which has not hosted a test since a game with India in 2014. No dates have been confirmed but the tour is likely to fall in a window during February-March.
"While we can't confirm it yet, it's something we're extremely interested in and working towards," New Zealand Cricket chief executive David White said in a media release on Friday.
New Zealand, who played the inaugural day-night test against Australia last year in Adelaide, had hoped to play their first at home early next year against South Africa but the idea was abandoned due to logistical problems.
South Africa's board are also mulling a pink ball test with Australia in Adelaide later this year but the Proteas' players have expressed their reticence.
New Zealand also confirmed three one-day internationals against world champions Australia from Jan. 30-Feb. 5 next year.
Bangladesh will tour for three ODIs, three Twenty20 matches and two tests from Dec. 26-Jan. 24.
The limited overs matches, like last year's series against Sri Lanka, will be held over the Christmas-New Year holidays.
South Africa begin their tour with a T20 international at Eden Park, where they were beaten by New Zealand in the semi-final of last year's World Cup, before they play five ODIs and three tests.
New Zealand will also host a full tour by the West Indies in 2017, limited overs series against Pakistan and three ODIs against Australia before the England tour.
New Zealand's 2016/2017 schedule:
Nov. 17-21 v Pakistan, 1st test, Christchurch
Nov. 25-29 v Pakistan, 2nd test, Hamilton
Dec. 26 v Bangladesh, 1st ODI Christchurch
Dec. 29 v Bangladesh, 2nd ODI, Nelson
Dec. 31 v Bangladesh, 3rd ODI, Nelson
Jan. 3 v Bangladesh, 1st T20, Napier
Jan. 6 v Bangladesh, 2nd T20, Mt. Maunganui
Jan. 8 v Bangladesh, 3rd T20, Mt. Maunganui
Jan. 12-16 v Bangladesh, 1st test, Wellington
Jan. 20-24 v Bangladesh, 2nd test, Christchurch
Jan. 30 v Australia, 1st ODI, Auckland
Feb. 2 v Australia, 2nd ODI, Napier
Feb. 5 v Australia, 3rd ODI, Hamilton
Feb. 17 v South Africa, 1st T20, Auckland
Feb. 19 v South Africa, 1st ODI, Hamilton
Feb. 22 v South Africa, 2nd ODI, Christchurch
Feb. 25 v South Africa, 3rd ODI, Wellington
March 1 v South Africa, 4th ODI, Napier
March 4 v South Africa, 5th ODI, Auckland
March 8-12 v South Africa, 1st test, Dunedin
March 16-20 v South Africa, 2nd test, Wellington
March 25-29 v South Africa, 3rd test, Hamilton
(Reporting by Greg Stutchbury; Editing by Ian Ransom)
