The Sydney Morning Herald has reported the four countries involved in the competition - New Zealand, Australia, South Africa and Argentina - have prioritised test rugby over resuming Super Rugby.
The report said Sanzaar is working on a "quickfire, six-week competition in one country, and likely one state or city".
Australia was viewed the most likely location due to its more lenient coronavirus restrictions compared to New Zealand and relatively low rates of infection compared to South Africa.
Perth was being touted as the ideal location because of its time zone.
The Rugby Championship was scheduled to begin on 8 August but that seemed doubtful with travel restrictions likely to be in force for the foreseeable future.
Rugby Australia said getting test rugby started is a priority for Sanzaar, adding there were still hopes this year's Super Rugby competition could be re-started.
However, in a short statement, New Zealand Rugby chief executive Mark Robinson said no decision had been made on any proposed competition.
"New Zealand Rugby is reviewing a range of competition options, both domestically and internationally, for when rugby is able to resume.
"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."