This week, a bill was introduced into Parliament providing more details into the mechanics of the marriage equality plebiscite, which could cost over $170 million.
In response, National Federal MP Andrew Broad suggested on Monday running the referendum on Indigenous recognition and the same-sex marriage plebiscite at the same time next year, alluding to the possibility to save up to $160 million.
However, back in May, Prime Minister Malcolm Turnbull had said a referendum on Indigenous recognition and a plebiscite on same-sex marriage wouldn't be held on the same day.
The Prime Minister has vowed to work with Indigenous leaders and the opposition leader to come up with a referendum question and an amendment to the Constitution, and has promised a national vote on changing the Marriage Act.
A council looking into the wording of the proposed referendum into Indigenous recognition in the constitution is not expected to report back until mid-2017.
On Wednesday, Prime Minister Malcolm Turnbull is moving a motion upholding equal rights for all Australians, and a commitment to reconciliation with Indigenous people to be debated next month.
Labor leader Bill Shorten wrote to Mr Turnbull at the opening of the new parliament proposing the bipartisan motion, but he'll be absent from parliament for the rest of the week, so the motion will be debated in October.