Senator Gallagher's office said on Tuesday an internal ALP investigation had cleared her in 2014, as part of the vetting process undertaken when she quit as the Australian Capital Territory's chief minister to join Labor's Senate team.

News Corp reports claimed Senator Gallagher had inherited Ecuadorian citizenship from her mother, who was born in the South American republic in 1943.

But the Labor frontbencher said on Tuesday she is not and has "never been" a citizen of Ecuador, despite her mother citing her place of birth as Ecuador on an Australian immigration entry card.

Senator Gallagher said her mother, Elizabeth Mary Gallagher, was a British citizen.

Under Ecuador's 2008 constitution, citizenship is automatically bestowed on people born overseas to a mother or father who were born in Ecuador, "up to the third degree of consanguinity [blood relation]".

But earlier versions of the constitution held that a person born to Ecuadorian parents could only acquire citizenship if they took up residence in the country, or expressed the desire to be Ecuadorian.

Under the 1929 version of the constitution – which was in effect when Senator Gallagher's mother was born – women were not automatically granted citizenship, but could apply for it once they turned 21. Senator Gallagher's mother left Ecuador as a child.

Senator Gallagher said that because the 2008 version of the constitution was not in place when her mother was born, she was in the clear.

"As part of the ALP vetting process, I disclosed that my mother was a British citizen, born in Ecuador to British parents, who were temporarily working in Ecuador," Senator Gallagher said in a statement.

"The circumstances of my mother's birth and citizenship were investigated. As a result of these investigations it was determined that I had not obtained Ecuadorian citizenship by descent from my mother. The 2008 Constitution was not in effect when my mother was born in 1943.

"I am not and have never been an Ecuadorian citizen."

Assistant Minister to the Treasurer Michael Sukkar said unlike other parties embroiled in the citizenship saga, Labor tried to "shut down" questions about the status of its MPs and senators. "Stop running this protection racket and come clean," he said.

The dual citizenship saga has so far led to seven members of Parliament facing referral to the High Court.

Under section 44, part (i) of the Australian constitution, a person is disqualified from standing for Parliament if they are "under any acknowledgment of allegiance, obedience, or adherence to a foreign power, or is a subject or a citizen or entitled to the rights or privileges of a subject or a citizen of a foreign power".

Last week the High Court, sitting as the Court of Disputed Returns, resolved to hear the cases in mid-October, prolonging the political uncertainty for months. Attorney-General George Brandis had sought for a September hearing, but was unsuccessful.

The court will consider if foreign citizenship meant Deputy Prime Minister Barnaby Joyce, LNP Senator Matt Canavan, One Nation senator Malcolm Roberts, and former Greens senators Scott Ludlam and Larissa Waters were not validly elected, while both Nationals senator Fiona Nash and key Senate powerbroker Nick Xenophon will have their cases referred when Parliament resumes on September 4.

Prime Minister Malcolm Turnbull said the government was "very, very confident" the High Court would uphold the eligibility of MPs and senators to remain in Parliament if they had unknowingly held a second citizenship by descent, and it would be "ridiculous" to conclude crossbench senator Nick Xenophon was English, and Deputy Prime Minister Barnaby Joyce a New Zealander, because of their parents' backgrounds.

Senator Gallagher moved to the federal Parliament in 2015, leaving the ACT Legislative Assembly to fill a vacancy created by the retirement of former senator Kate Lundy.

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