The declaration was circulated on Tuesday after former territory speaker Vicki Dunne publicly questioned whether members may have been "provided with information that was inaccurate" when Senator Gallagher was nominated to fill a casual vacancy in early 2015.

The Assembly is this week expected to debate an Opposition motion to establish a select committee to investigate whether Senator Gallagher may have unintentionally misled the chamber.

The former chief minister renounced any entitlement to British citizenship just before the 2016 election, acting on advice from Labor officials as she nominated for re-election.

It is not clear whether she was eligible to fill a casual vacancy from March 2015 until she was elected in her own right in 2016.

While any potential breach would not come before the High Court as it was during a previous parliament, the issue has brought into question processes from both the Assembly and the Labor Party.

A second motion from Mrs Dunne could also see the Assembly set up a administrative inquiry into nominations for future vacancies.

Mrs Dunne, who was speaker at the time of Senator Gallagher's nomination, said she was concerned about the process and that she may have overseen a potentially wrong or misleading declaration.

She said while she did not believe the declaration was intentionally inaccurate at the time it was signed, the Assembly needed to know that its processes were "not subject to contempt" and could not result in potentially misleading the Governor-General.

Mrs Dunne previously wrote to Speaker Joy Burch urging her to examine whether Senator Gallagher's nomination should take precedence over other Assembly business, a request Ms Burch rejected.

Ms Burch also rejected an earlier request from Mrs Dunne for an administrative inquiry into the Assembly's process for filling casual Senate vacancies in a letter in October.

Chief Minister Andrew Barr said Mrs Dunne's motion was about seeking "to maximise a political outcome", rather than addressing an issue he believed was the remit of the federal parliament.

While Greens leader Shane Rattenbury, representing the key votes, said the minor party did not support suspending business to vote on the motion on Tuesday, he said the two motions should be debated together on Thursday.

Senator Gallagher has refused to say when moves to renounce entitlement to UK dual citizenship were officially confirmed by British authorities.

Labor's spokeswoman for small business and financial services revealed in September that she could have been in breach through a possible entitlement by descent through her father, Charles Gallagher.

Senator Gallagher said she took no action to renounce any entitlement to foreign citizenship after replacing Kate Lundy in the upper house, only later renouncing any entitlement "out of an abundance of caution".

Recent High Court rulings have led to speculation Senator Gallagher might not have received formal confirmation before the June 9, 2016 deadline for candidates to declare to electoral authorities they were not dual citizens.

She submitted the required paperwork to the UK Home Office and made the required payment on April 20, 2016.

Earlier this month, former Home Office lawyer Phillip Gamble said Senator Gallagher would have been a British citizen when she first took her seat.

He said if Senator Gallagher's father was born in the UK she would have acquired British nationality by operation of law at her birth.

In the 1990s, Senator Gallagher made investigations about taking up British citizenship but abandoned the plan when her father became ill.

She was advised that submitting the declaration of renunciation with the Home Office meant she had taken "all reasonable steps to renounce any entitlement to British citizenship".

Senator Gallagher said she never took any steps to gain British citizenship and believed she was not a dual citizen

"When the Turnbull Liberal government has cut funding for local hospitals by $35 million, cut funding for Canberra schools by $20 million and sacked thousands of hard-working public servants, it's disappointing that the only priority for the Canberra Liberals is to pursue a cheap political stunt like the one they pulled this morning, instead of standing up for the issues that matter to the people of the ACT," she said.