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But the New Zealand Government says talks between the two countries are ongoing and no firm date has been set for a travel bubble.
Australian media organisations today reported that New Zealand Prime Minister Jacinda Ardern would announce the transtasman bubble when she swore in her Cabinet next week.
The reports in the Daily Mail and The West Australian, which cited West Australian government sources, said the travel arrangements would be in place by Christmas at the latest.
Ardern's office has been asked for comment.
A Ministry of Foreign Affairs and Trade spokeswoman said discussions were still continuing on New Zealand-Australia travel.
New Zealand remained committed to introducing two-way trips as soon as it was safe, but a start date was yet to be decided, the spokeswoman said.
"There will be a range of health and border requirements that need to be met before New Zealand can allow quarantine-free travel from Australia."
It is not the first time Australian media have reported that a travel bubble was about to be introduced. In early October, Ardern poured cold water on a suggestion that two-way travel was "days away".
"In our view we are not ready to have quarantine-free travel with Australia. They have a very different strategy to us, and so they're making that decision ... but for now we of course have to keep our New Zealanders safe."
She also said she hoped to have some sort of transtransman travel arrangements in place by the end of the year.
New Zealand's borders have been closed to international travel since March, except for returning New Zealanders and exemptions for health workers and some key industries.
Last month, New South Wales and the Northern Territory started accepting travellers from New Zealand without requiring them to quarantine.
But that is a one-way arrangement. Kiwis returning to New Zealand still need to do their 14-day stint in managed isolation. And Australian tourists are not able to travel to New Zealand.
Next week, Queensland plans to reopen its border with New South Wales, which could mean that the state would be opened to New Zealand travellers.
However, the Greater Sydney region was exempted from that agreement because of concerns about mystery Covid-19 cases that could not be linked to known clusters.
Australia's Federal Tourism Minister Simon Birmingham said earlier this week that quarantine-free travel between the two countries would be recognition of how well both countries had handled Covid-19.
"I welcome the fact Prime Minister Ardern has made some positive comments about opening up in a reciprocal way with Australia, and I hope that we can see this facilitated by the year's end," he said.
At last count, Australia had an estimated 200 active Covid-19 cases and New Zealand had 68 cases.
Nearly 2000 New Zealanders have entered Australia since the borders were relaxed in two states.
But the move has been controversial, because New Zealanders were found to have travelled domestically to states which did not opt into the travel bubble, including Victoria, South Australia, Western Australia and Tasmania.