NZC chief executive David White said the England test was something they were pursuing and it will mark the return of test cricket to Eden Park, which last saw a five-day game in 2014 against India.
"While we can't confirm it yet, it's something we're extremely interested in and working towards," White said.
The schedule announced yesterday will see 98 days of international cricket and is highlighted by back-to-back Chappell-Hadlee series as well a tour by South Africa.
The summer of 2016-2017 will see Pakistan and Bangladesh the first to visit New Zealand in an overall schedule comprising seven tests (three South Island, four North Island), 11 one-day internationals and four Twenty20 internationals.
Pakistan will play two tests, followed by Bangladesh who will play three T20 (one in Napier), along with three ODIs and two tests.
Auckland, Napier and Hamilton will then host Australia for the Chappell-Hadlee games, all within six days, before the marquee tour of South Africa featuring one T20, five ODIs (including one in Napier) and three tests.
The 2017-18 schedule sees Pakistan return and Australia back for another Chappell-Hadlee series, as well as tours against the West Indies and England.
Five tests (three North Island, two South Island), 17 ODIs and 5 T20Is puts it on track to be one of New Zealand's biggest international summers on record.
The West Indies will arrive in November 2017 for three tests, five ODIs and one T20I, before a clash in the shorter formats against Pakistan with three T20Is and five ODIs. Australia then arrive for their third-straight year of the Chappell-Hadlee rivalry, followed by England for five ODIs and two tests.
"The last couple of years has seen a significant rise in interest in cricket and I think the schedule we've locked in will help that interest continue to grow," said White.
"We're really pleased how much of the country we've been able to cover with the schedule, with a strong North and South Island split," he said. "Both will see a lot of test cricket over the next two years and that's been driven by the feedback from the fans."
He said the desire both of major associations and local councils around the country to be involved in international cricket has never been higher.
The Black Caps next play against Zimbabwe and South Africa in July.
The New Zealand women's cricket side's schedule will be announced in the coming weeks.