The Australian cricketers were already considering a boycott of the scheduled T20 game against the Black Caps in Auckland before it was moved to Wellington.
That's according to Australian media reports who have quoted the Aussie spinner Ashton Agar as saying Covid-19 ramifications are testing the players' mental and physical state.
The Daily Telegraph said some state governments had classified Auckland as a "red zone" meaning automatic quarantine, with no exemptions possible, for people returning to Australia.
Agar said: "We have faith in cricket Australia and New Zealand Cricket that they have the players' physical and mental health in their best interest.
"They've made sure that they've looked after the players' mental and physical wellbeing and come to the right decision.
"COVID moves so quickly and we have to move with that.
"It's not the ideal situation…no one really likes the thought of quarantine.
"There's a lot of guys who have done up to six weeks of isolation and quarantine, maybe more, and they've got more coming up.
"Cricket doesn't stop throughout the year and with this situation, there seems to be a lot happening.
"We've had a briefing, management has kept us up to date. We have to look forward to the games that are coming up, and that's all we can do at this point in time."
New Zealand lead the series 2 - 0, with the three remaining games all to be played behind closed doors in Wellington which is under level two restrictions this week.
When asked how it had affected the team, Black Caps coach Gary Stead said it hadn't changed their planning.
"It's out of my hands so I choose not to be frustrated about it," Stead said.
"In many ways, as the coach of the team, it's easier. We're settled here in one place, it's less travelling and that comes as a little bit of a luxury.
"At the end of the day it just comes down to individual's attitudes and how they respond to it... in this Covid-era, we need to adapt and it's something we pride ourselves in."
Stead said they were treating each game as its own and wasn't getting carried away by their lead.
"You know that's there, but again, to beat them is tough," he said. "[Australia] don't lie down, they don't go away and in the first two games we had to be somewhere near our best and I think we're going to have to be that again."
Game four was scheduled for Eden Park in Auckland, which is in a level three lockdown.