Wright announced his departure today and said the upcoming tour to the West Indies in June would be his last international assignment with the New Zealand team.
He began his tenure in December 2010 and despite being well liked by the players he appeared to be at odds with the national body's director of cricket John Buchanan about the direction of the side.
Wright was offered a contract through until the 50-over World Cup in 2015, to be co-hosted by New Zealand and Australia, but couldn't commit and it is understood that his differences with Buchanan were a major stumbling block.
New Zealand's future tours programme is packed through until 2020, which prompted White to not rule out dual coaches or more.
"That's a possibility moving forward and I know that other countries are looking at that scenario,'' he said.
"We've got limited resources compared to other countries. I don't know how many coaches England have got and support staff, but it's massive.
"It's incredibly demanding [to be an international coach] ... It's got tougher than it was.''
The suggestion that there could be more than one coach of the national team seems outlandish but could become a reality given the gruelling travel schedule and overdose of matches on the international calendar.
Another scenario could involve coaches - either assistants or the top dog - not taking part in certain tours, something which South Africa have embraced. On their recent tour of New Zealand, bowling coach Alan Donald left early for a break.
Former test opener Mark Richardson said finding a replacement for Wright of international quality would be tough given what little money New Zealand Cricket would be able to offer in comparison to countries like Australia or England.
"It's a difficult one when it comes to finding a coach for New Zealand because we are not one of the rich nations,'' Richardson said.
"We can't afford to pay our coach that much. So if we want to get a guy with a recognisable coaching record with international experience and you know he's a top quality coach it's fairly tough because you've got to pay decent coin for those guys.''
Richardson said those coaches want to make sure they are also available for their IPL responsibilities, and if they were locked up for New Zealand they would not be able to do that.
"So I think we need to think outside the square a little but. We will probably have to end up taking a bit of a punt and look for an up-and-coming coach and that could be anyone really, couldn't it?''
Within the domestic ranks, Northern Districts mentor Grant Bradburn, Auckland's Paul Strang or Wellington's Jamie Siddons appear the more attractive options, while national assistant Trent Woodhill is highly thought of.
If it came down a domestic coach stepping up, Bradburn could have the inside running as White said they would prefer to promote a Kiwi for the role, which would count against Zimbabwean Strang and Australian Siddons.
"First and foremost we want the best coach. Ideally that person would be a New Zealander in a perfect world,'' White said.
