Wright has declined an offer to extend his contract and will step down as coach following the tour of the West Indies.
Wright's decision is a huge disappointment to New Zealand Cricket, which had hoped to retain his services. The former opening batsman has achieved some memorable results since assuming the role in late 2010.
Under his guidance, the Black Caps reached the semifinal of the World Cup and recorded a historic test win against Australia in Hobart this summer. It was New Zealand's first test win against Australia across the ditch in 26 years.
His successor can look forward to a challenging future with tours to India, Sri Lanka, South Africa and home-and-away series against England.
Johnson dismissed any suggestion he might apply for the job.
"I've still got a year left with Otago so that is what I'm concentrating on," he said.
Of the local coaches, Johnson firmly believes Carter is the best option.
"He has been involved in the setup before [both as New Zealand A coach and Black Caps batting coach]. He knows and understands players really well.
"He is very experienced. He has coached a county side before and is one I think could do the job.
"Whoever the new coach is they have to get on well with the captain [Ross Taylor] and the captain has to get on well with him," Johnson said.
"The players have to respect the new coach so there is a lot of things to consider before the next person steps in to the role.
"In this day and age the players have a lot of say in what track you go down."
Auckland coach and former Zimbabwean international Paul Strang has had some good results with his provincial side.
The Aces won the domestic twenty/20 tournament this season and reached the final of the one-day tournament.
Under Grant Bradburn's leadership, Northern Districts won the Plunket Shield in 2009-10 and again this summer.
Wellington and former Bangladesh coach Jamie Siddons has the credentials to do the job.
Former Otago coach Mike Hesson, who has also coached New Zealand A sides and is currently coaching the Kenyan national team, had some good results during his six-year stint with the Volts.
But in an email to the Otago Daily Times, Hesson indicated he was unlikely to apply.
"To be honest, I hadn't even considered it," he wrote.
"I have only been back a couple of weeks and we have our own security issues to deal with at the moment over here, so as you can understand that is my priority at present."
Meanwhile, New Zealand Cricket chief executive David White has not ruled out the possibility of having different national coaches across the three forms of the game given New Zealand's future tours programme is packed through until 2020.
"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."
