"So we've commenced discussions with the Government about that."
However, Prime Minister Jacinda Ardern told media on Monday that she had not had any conversations with NZC.
She did acknowledge the situation though, saying "we know it's an issue."
"We will be weighing up all the factors," she said when asked if sports teams will be prioritised.
"We have a number of different groups that may have the job of representing New Zealand abroad who will be asking for advice on how to manage vaccine in amongst that.
"So that's something we need to give consideration to, we haven't made decisions yet."
Government Cabinet ministers have received advice regarding a nationwide vaccination schedule but have yet to finalise or publish a complete plan.
Covid-19 Response Minister Chris Hipkins said last week that frontline health and emergency workers would be up next, after border workers and their families, but further decisions had yet to be signed off by Cabinet.
When asked in February about the possibility of athletes who required international travel, to events such as the Olympics, receiving vaccinations before the general public, Ardern avoided a direct answer.
"That's a conversation for further down the track," she said. "We are focusing on those domestically who are at the greatest risk."
After completing a home series of ODIs and T20s against Bangladesh on the first of April, some of New Zealand's top players are set to travel to India to take part in this year's Indian Premier League beginning April.
Those players - some of whom expect to spend up to 10 months overseas in 2021 - will then join a wider squad in England in May to begin a tour that includes two test matches against England and the World Test Championship final.
Following the England jaunt there is a return to Pakistan, the World T20 in India and a tour of Bangladesh where every port of call carries the risk of players contracting Covid-19 and putting those fixtures in jeopardy.