Canberra MP Alicia Payne and her Darwin-based colleague Luke Gosling have agreed to co-sponsor private member's legislation to repeal the Andrews Bill, under a plan thrashed out ahead of Parliament's return on July 26.

Opposition Senate leader Simon Birmingham has promised to support the bill and is vowing to help smooth the path for it be debated in the upper house.

As the rare conscience vote looms, advocates and opponents are also preparing to ramp up their lobbying of federal politicians in the hopes of swaying those sitting on the fence.

Leading advocacy group Go Gentle Australia has said it would be a "very brave" Federal Parliament to reject the bill, given a national trend that has seen assisted dying passed in every state since 2017.

Labor politicians from the ACT and NT have stepped up talks since the May 21 election about which them of would introduce a bill to overturn the ban, after Anthony Albanese pledged to prioritise debate on it if he swept to power.

While no date has been set, momentum is growing for debate and a vote to be held in the first sitting fortnight.

Mr Gosling, who represents the seat of Solomon, said he "couldn't think of any reason" why a bill couldn't be put for debate in the "first couple of sitting weeks".

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The Canberra Times understands that if for some reason a co-sponsored private members' bill is not allowed, one option would be for Mr Gosling to introduce it himself, and then for Ms Payne to second it.

Whatever form it takes, politicians from the two territories are adamant the responsibility of introducing the bill should be shared.

"All Australians should have equal democratic rights, whether they live in Canberra or Queanbeyan," Ms Payne said.

"That's why I will introduce a private member's bill, with my Northern Territory colleague Luke Gosling, to repeal the Andrews Bill as soon as possible when parliament resumes."

"The reality is the Andrews bill makes residents of the ACT and NT second-class citizens, and I'm proud the Albanese Labor government will enable the parliament to vote on restoring territory rights."

A conscience vote is set to be granted to members of the major parties, meaning the outcome is harder to predict.

A number of Labor figures - including right faction heavyweight Don Farrell - voted against lifting the ban when David Leyonhjelm's bill was defeated by just two votes in 2018.

Mr Gosling was among the ACT and NT representatives who last year pushed against Labor granting a conscience vote, arguing the bill was about territory rights rather than voluntary assisted dying.

Mr Gosling, who has strong reservations about assisted dying, said educating his colleagues about that distinction would be his focus ahead of the vote.

Asked if he believed the bill would be pass, Mr Gosling was upbeat.

"I've got a growing confidence that the education process ... is starting to sink in," he said.

Opposition from some Labor members is likely to mean that Coalition votes are needed for the bill to pass through the upper house.

Leading moderate Simon Birmingham and NSW senator Andrew Bragg are among the Coalition members who support territory rights.

Senator Birmingham told The Canberra Times that the passage of assisted dying laws in each state had made the case to overturn the Andrews bill "more compelling".

"I have long supported the principles behind carefully designed voluntary assisted dying legislation," he said.

"As a Liberal I see this as a matter of empowering individuals to make informed choices about their lives".

Senator Birmingham has offered his "full support" to a bill, which includes backing any procedural steps needed to allow a vote to go ahead.

Senator Bragg said it was a "missed opportunity" that the matter wasn't dealt with in the previous parliament, when NT Country Liberal Sam McMahon put forward a bill but it never reached a vote.

Former Prime Minister Scott Morrison had no intention of allowing debate on a repeal bill if he had managed to secure another term.

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