Earlier, Cricket Australia said there is a plan to get them out of the pandemic-ravaged country by chartered flight 'in the next two or three days'.
"What the BCCI are working to do is to move the entire cohort out of India where they will wait until it's possible to return to Australia," CA interim Chief Executive Nick Hockley told reporters in Sydney.
"That's now narrowed down to the Maldives and Sri Lanka. The BCCI are committed not only to the first move, but also to putting on a charter to bring them back to Australia."
The CA official refused to speculate if the league could resume this year.
"I think it's premature to speculate on that," he said.
"At the moment, the BCCI are very focused on getting all the players, not just the Australians, home safe."
Players' union boss Todd Greenberg said the cricketers are under an "enormous amount of stress" in India.
"The public will see our best Australian cricketers as almost superheroes ... but they are human beings," the chief executive of the Australian Cricketers' Association said.
India's coronavirus deaths rose by a record 3,780 during the last 24 hours, a day after it became the second country to cross 20 million infections, after the United states.
While the Indian cricket board (BCCI) has promised safe passage for the players and officials, New Zealand Cricket said all of their players were isolating in team hotels in India.
An NZC spokesman said captain Kane Williamson and several of his team mates had already been booked to join rest of the test side in England next month.
"We haven’t got the finer details of that sorted yet. We’re working now with the ECB (England and Wales Cricket Board) and BCCI to arrange flights to get them over to England," the spokesman said.
New Zealand players' union boss Heath Mills said the cricketers were 'pretty anxious now and pretty keen to come home'.
"They are working with their IPL franchises and some franchises have been good at assisting and others haven’t," Mills told media.