Rugby Australia's general manager of professional services Ben Whitaker told the Sydney Morning Herald that getting test rugby started was a priority for Sanzaar.
"There is definitely a collective commitment to prioritising test match footy," Whitaker, who has been in discussions with other Sanzaar nations, said.
"But we are also committed to community safety, first and foremost. We roll off the back of that. But we are ready with different formats. Hopefully that's sooner rather than later."
Whitaker also said there are still hopes for a resumption of Super Rugby.
"The other thing we are committed to is trying to get some Super Rugby played as well," he said. "As you squeeze towards the back end of the year, you have to have various models to handle that."
New Zealand Rugby later responded to the report saying no decision has been made on any proposed competition yet.
"New Zealand Rugby is reviewing a range of competition options, both domestically and internationally, for when rugby is able to resume," Chief Executive Mark Robinson said in a statement.
"However nothing has been decided and any decisions will be made in alignment with advice from the Government. At this stage any competition options are purely speculative."
Another report in South African newspaper Rapport revealed that the Springboks believe the Rugby Championship will start in August or September.
However, the Australian report played down that suggestion with travel restrictions still likely to be in place for the foreseeable future.
The Rugby Championship was scheduled to begin on August 8, with the All Blacks facing the Wallabies in Melbourne and the Springboks taking on the Pumas in Johannesburg.
• Covid19.govt.nz: The Government's official Covid-19 advisory website