But Senator Reynolds has now revealed her own views in comments to Fairfax Media.
“While I will not pre-empt the findings of the committee, it is my personal belief that the cleanest way to resolve this problem is to remove sections of 44,” she said.
“Section 44 has unintentionally created two classes of Australian citizenship.
“The only way to do that would be through a referendum. Ultimately the issue of dual citizenship for MPs must be one for Australians to decide, not a parliamentary committee.”
Section 44 of the Constitution contains a number of smaller sections that disqualify certain people from being elected, including those who are bankrupt or who hold an “office of profit under the Crown”.
But the best-known is Section 44(i), the dual-citizenship rule, which sensationally ended the political careers of eight senators in the last 12 months.
It also triggered by-elections that threatened the Turnbull Government’s one-seat majority in the House of Representatives, after the High Court ruled former Nationals leader Barnaby Joyce and Liberal MP John Alexander were invalidly elected. Both men won their seats back.
Senator Reynolds, herself a veteran, reportedly told Fairfax Media it was inconsistent that dual citizens could serve in the Army but not sit in the parliament.
"Not only is this out of step with other areas of contemporary Australian life, it's also out of step with most western democracies which allow dual citizens to serve in Parliament, including the UK, US and Canada."
In August last year, a Guardian Essential poll found only 41 percent of Australians supported allowing dual citizens to sit, compared with 40 percent saying “no” and 18 percent saying they did not know.
Other Coalition MPs like Craig Laundy have publically suggested a referendum.
But prime minister Malcolm Turnbull has previously said a referendum would likely fail.
“I think it's questionable whether Australians would welcome dual citizens sitting in their Parliament,” Mr Turnbull said last year.
Opposition leader Bill Shorten said the dual-citizenship rule should not have been included in the Constitution "in the first place", speaking with reporters in Sydney.
But he said it was a more urgent priority to hold a referendum on replacing the British monarch as Australia's head of state or on Indigenous recognition in the Constitution.