White has returned home to Canberra after sustaining an MCL injury during training at their Gold Coast camp, and To’omua is already there with his injury checked out by Rugby Australia chief medical officer Warren McDonald.
To’omua is expected to join the squad on Sunday and the Wallabies are hoping the playmaker will be available for the first test on July 7.
O’Connor, who carried the Super Rugby Trans-Tasman injury, is managed through training but the five-eighth is expected to play.
With White out, Queensland’s Tate McDermott is now set for his first test start after two games off the bench, while Brumbies No.9 Ryan Lonergan is set to make his debut.
Waratahs half-back Jake Gordon is at camp but is also recovering from an MCL injury and remains an outside chance to be available.
White does not need surgery and medical staff will be hopeful he will be part of the Bledisloe Cup with the opener on August 7 in Auckland.
It comes as Rugby Australia is moving forward with plans to play the opening three-round match against France at SCG despite the COVID-19 outbreak in Sydney.
The French team of 42 men arrived in Sydney on Tuesday evening and underwent COVID-19 tests on Wednesday.
The Blues will be quarantined in their hotel for the next fortnight, but they will be allowed to train before the July 7 test at the SCG.
The teams play a condensed series with three tests in 11 days, the second at AAMI Park in Melbourne on July 13, followed by the third at Suncorp Stadium in Brisbane on July 17.
The second test appeared to be the most dubious, with Melbourne locked out for two weeks after an increase in COVID-19 cases, but that eased with crowds returning to sporting events this weekend.
There were questions about whether that game would be moved to Canberra, which could now be an option for the Sydney game if the pandemic continued to worsen on the east coast.
Queensland and Victoria have closed their borders to NSW residents in sensitive areas of the eastern suburbs and central Sydney.
RA chief executive Andy Marinos said he remains hopeful the matches will go as planned.
“Knowing that we continue to operate in a dynamic environment with impacts from COVID-19, we are moving forward with our plans to host these matches as planned, subject to any further advice from our state government partners” , Marinos said in a statement.
“We’re just two weeks away from the start of the series which will begin with the Wallabies’ first game at the historic Sydney cricket ground in 35 years.
“I would like to thank (the president) Bernard Laporte, (the coach) Fabian Gautier and the FFR (French Rugby Federation) for their partnership so that this series can take place.
“It has been a colossal effort on the part of everyone involved. ”