The Greens want voters to be able to cast preferences "above the line" on the Senate ballot paper.
The idea is contained in the minor party's proposal put to Labor, the coalition and crossbenchers as the government considers Senate voting reform ahead of the next election.
Greens electoral matters spokeswoman Lee Rhiannon said allowing voters to allocate at least six preferences and scrapping group voting tickets was better for democracy than "backroom deals" between parties.
The party has yet to decide whether to support changing "below the line" voting.
At present, a voter must number every box below the line of the Senate ballot paper, if they don't put a "1" above the line.
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A proposal gaining some support is to allow voters to cast preferences below the line which match the number of vacancies - one to six in a half Senate election and one to 12 at a full Senate poll.
The Greens will oppose any changes to party membership rules which would make it harder for small and emerging parties to register.
It is understood acting Special Minister of State Mathias Cormann was involved in talks on electoral reform over the past week.
Sealing a deal on Senate voting reform will be the job of whoever takes over the ministerial role permanently in the reshuffle to be unveiled by Prime Minister Malcolm Turnbull within days.
Liberal Democrats senator David Leyonhjelm said he understood Labor was divided on the way forward and the government was still weighing up the risks of changing the system before going to a double-dissolution election.
"The question for the government is whether they would be better off than they are now," he told AAP.
He said a double-dissolution election under new Senate voting rules could lead to a "permanent logjam" between Labor, the coalition, the Greens and potentially one crossbencher, South Australia's Nick Xenophon.
