Prime Minister Jacinda Ardern says the Government is doing everything it can to host All Blacks tests in New Zealand but admitted it is "not just down to us".
An All Blacks squad was named yesterday, with hopes of test matches against at least Australia and a Pacific team, and possibly hosting the Rugby Championship later this year.
New Zealand is hoping to host Australia, Argentina and South Africa in the four-nation competition in November and December.
However, doubts have emerged over the logistical difficulties of securing locations for visiting nations to train while in quarantine, as strict border restrictions continue due to the pandemic.
News over the weekend that six players from the Pumas tested positive for Covid-19 added fresh doubts over the likelihood of the tournament going ahead.
NZ Rugby is more hopeful of a Bledisloe Cup series against the Wallabies but that has also been complicated by border restrictions and a resurgence of the virus in both countries.
Speaking to Newstalk ZB, Ardern said All Blacks tests are "a real possibility" but warned that the issue is not solely in the Government's hands.
"There have been some discussions of whether we could play host for a tournament," Ardern said.
"It's something we have been exploring, and seeing whether we can facilitate that within current arrangements. We do have tight arrangements at the border that we need to uphold; [the department of] health need to be happy with everything.
"It's not just down to us. We are doing enough to make it a real possibility. We have kept that door open and in good faith gone through those protocols. But ultimately we are not the only ones making that decision."
Meanwhile, All Blacks coach Ian Foster remains optimistic about the prospect of tests, at least against Australia, this year.
"There's a lot of different spreadsheets, a lot of people smarter than me coming up with options," Foster said. "Right now our plans are really clear.
"We think within a week we'll have more certainty. We're extremely hopeful of some tests with Aussie and after that we're not too sure."