Labor and the coalition could come to an agreement on changing the Senate election system before the next election.
But shadow attorney-general Mark Dreyfus says while the opposition is in favour of change, it is up to the government to bring forward its plan as soon as possible.
Labor is in talks with the government on which parts of a May 2014 report by the parliament's electoral matters committee to implement.
The committee's report - the findings of which were endorsed by Labor, the Greens and the coalition - said voters should be able to mark preferences above the line on Senate ballot papers, and not have to number all the boxes below the line.
Voting above the line hands the flow of preferences over to the parties that lodge "group voting tickets" with the Australian Electoral Commission.
There have been concerns that group voting tickets have been exploited by small "pop-up" parties, enabling candidates to win with a tiny proportion of the vote.
At the 2013 election, Australian Motoring Enthusiast Party candidate Ricky Muir won a Victorian Senate seat with only 0.51 per cent of the primary vote.
"The opposition is talking with the government and we are talking among ourselves as to what is the right way to reform Senate voting processes," Mr Dreyfus told ABC radio on Wednesday.
"It's a matter for the government to put forward that proposal - we are hoping that occurs soon."
Liberal senator Ian Macdonald, a member of the electoral committee, said the government should act on the report before the next election due in September.
"The people of Australia have indicated something needs to be done," he told AAP.
Australian Motoring Enthusiast Party senator Ricky Muir suggested there be no party branding on ballot papers.
"No above the line (voting) and change the rules to one-to-12 below the line," he said.
Independent senator John Madigan said changing the system would leave political power in the hands of a "cartel" of major parties.
Fellow crossbench senator Nick Xenophon is more supportive of change and is preparing to introduce his own reforms to parliament.
These would include getting rid of group tickets.
Liberal Democrats senator David Leyonhjelm said he had spoken with the minister responsible for electoral matters, Mathias Cormann, who gave no indication he wanted to get rid of group voting tickets.
"Unless he is the world's best poker player I don't believe that is on his agenda," Senator Leyonhjelm told Sky News on Wednesday.
"But certainly they are looking around for some changes to be made."
The senator is comfortable with the idea of allowing voters to cast a ballot for only six candidates below the line in a half-Senate poll and 12 in a full Senate election, rather than having to fill out all the boxes.
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