The novel coronavirus pandemic has kept administrators on the back foot trying to nail down plans for the annual test championship involving South Africa, New Zealand, Australia and Argentina.
Such is the uncertainty, All Blacks coach Ian Foster named his first squad on Sunday even though there is little sense of when the team might play beyond tentative plans for Bledisloe Cup matches against Australia next month.
SANZAAR has released little information since saying in July that they were keen on hosting the championship in a 'hub' scenario in the November-December test window.
It gave a likely location of New Zealand following the country's early success in containing the pandemic, but last month's resurgence of infections in Auckland may have opened up other possibilities.
New Zealand Prime Minister Jacinda Ardern said this week she was still keen to host the tournament, but noted the choice of venue would not come down just to her government.
"I think we're doing enough to make it a real possibility," she told radio station Newstalk ZB.
"We've kept that door open in good faith, gone through all those protocols, but ultimately we're not the only ones making that decision."
The Sydney Morning Herald said on Wednesday that SANZAAR was now possibly considering Australia as the host nation.
Administrators have also had to contend with six Pumas players testing positive for COVID-19 as the Argentine team entered a bio-secure bubble last week.
The Pumas and world champion Springboks have not played since March when the international edition of Super Rugby was postponed, although South Africa are hoping to launch a domestic competition next month.
The hosting uncertainty has prompted frustration from New Zealand pundits, who watched fans flock to their domestic Super Rugby competition before social distancing restrictions were reimposed last month.
"We've made all this sacrifice to make (New Zealand) the safest country in the world and what is happening?," former All Blacks winger John Kirwan told Sky Sports on Tuesday.
"I also want to know why New Zealand Rugby is not putting some pressure on. Why are we quiet? Where is our transparency, people? We need to know."