The All Blacks' tests against Wales in July seem even less likely to proceed, with up to five Welsh players now demonstrating coronavirus symptoms.
Wales, who still have to complete their Six Nations campaign, are scheduled to play Japan on June 27, before heading to New Zealand to face the All Blacks on July 4 and July 11.
Earlier this month, Pivac revealed three unidentified players had contracted the virus, but had since recovered.
Now that number has increased, with Pivac admitting four or five of his Six Nations party had been unwell with COVID-19 symptoms.
"It does seem unlikely, and as each day and each week goes by, that seems more and more the case," says NZ-born coach Wayne Pivac of the All Blacks series.
"But until it is called off or postponed, we have to prepare as if it's going ahead and that's certainly what we are doing.
"We have been very, very lucky, very fortunate, that no-one’s been seriously ill with the virus.
"I have spoken to all the players from the Six Nations squad individually more than once, since the lockdown.
"I know who’s well and who’s picked up any sort of illness - there's about five players all up.
"No-one has been required to go to hospital. They have had symptoms, such as coughs and a temperature, so they have dealt with that at home and they have come out of the other side."
The former Auckland and North Harbour coach succeeded current Chiefs coach Warren Gatland as Wales boss, opening his account with a 42-0 win over Italy in Cardiff, before losses to Ireland, France and England.
Even though rugby has stopped, Pivac feels there is a silver lining to the hiatus.
"The feedback from a lot of them is that they are feeling great from having had a break, because they had pre-World Cup camps, a World Cup, back into club rugby and back in international rugby again, so their bodies were pretty beaten up.
"A lot of them are feeling really good, both mentally and physically, from having time off."
Along with the two tests against Wales, the All Blacks are due to face Scotland on July 18.
