"Due to the ongoing flight suspension, we are considering arranging a third special flight to Colombo to allow passengers to travel by commercial means to Melbourne," said the High Commission in a message.
The third flight is scheduled to depart Dhaka on May 27.
The High Commission says they need a minimum of 120 full fare passengers to ensure this flight goes ahead.
It said they cannot guarantee that they will be able to organise any further special flights following the departure of the third flight.
The flight is only open to Australian passport holders, Australian permanent visa holders and their spouses, legal guardians or children.
At this stage most scheduled passenger flights to and from Bangladesh remain suspended.
The flight suspension is planned to last until May 30, but it has been extended a number of times and may be extended again, said the High Commission.
They have emailed everyone already registered with then with details about a possible third flight.
"We strongly encourage you to book a seat on the third flight to ensure you can return home as soon as possible," the message reads.
On May 9, a non-scheduled Sri Lanka Airlines flight left here for Melbourne with 220 Australian citizens and their families.
The special flight also carried eight New Zealand citizens and permanent residents on their way back to New Zealand.
Together with 285 passengers who departed from Hazrat Shahjalal International Airport on April 16, over 500 have so far returned to Australia, said the Australian High Commission in Dhaka.
Since the COVID-19 pandemic began, the Australian government has helped over 15,000 Australians to return home from overseas, including from cruise ships and by using one-off arrangements with commercial airlines.