New Zealand Cricket (NZC) has confirmed negotiations with Jacinda Ardern's government to protect the Black Caps before they head overseas next month and attempt to become the inaugural world test champions.
"We've had very positive discussions," Mr White told AAP.
"The government has got a scheme for workers who travel overseas, there's a possibility to get vaccinated.
"So we've commenced discussions with the government about that."
Unlike Australia, the NZ government has yet to confirm or announce its full vaccination rollout plan.
It is currently vaccinating border workers, their families, and is moving on to front-facing health workers next.
Vaccination of the general population is expected to begin in the second half of the year.
Asked last month about the possibility of touring athletes - which will soon include Olympians and Paralympians - receiving vaccinations ahead of the general population, Ms Ardern deferred.
"That's a conversation for further down the track," she said.
"We are focusing on those domestically who are at the greatest risk."
It is natural that NZC would seek to inoculate their stars, given their touring schedule in the next three months includes India and England.
Those two Covid hotspots are recording more new cases each day than NZ has experienced in total.
For the Black Caps, fresh from their 3-2 series win over Australia on Sunday, the vaccinations will need to come soon.
Several high-profile test players, including Williamson, Trent Boult and Kyle Jamieson, are due on the subcontinent for the Indian Premier League (IPL), which begins on April 9.
They won't return home after the IPL, instead heading straight on to England for two test matches and the World Test Championship final against India in June.
As the Pfizer vaccine currently being administered in NZ requires 21 days between the two vaccinations, those jabs will need to be prioritised this week if they are to fulfil their cricketing obligations.
Mr White said the chance to be the first world test champions was a tremendous opportunity.
"It's fantastic. We're so excited. The team has done fantastically well to qualify," he said.
"To play in the inaugural championship and to play against India is huge, the global exposure. Our guys are really excited at the opportunity."
