Western Australian Liberal senator Dean Smith says he wants same-sex marriage passed through the parliament this year.
He's been drafting a bill in secret, and now plans to reveal it to the Coalition partyroom.
But his senate colleague Eric Abetz, a staunch opponent of same-sex marriage, says he's confident the rest of the government remains committed to holding a plebiscite.
"I would assume that the partyroom would be saying that we have gone to the last election with a firm policy for a plebiscite, and if the parliament wants to deny the Australian people their voice in changing society's foundational insitution, namely marriage, if parliamentarians think they know better on such a fundamental issue than the Australian people, it sadly tells you everything you need to know."
Speaking from Paris, Prime Minister Malcolm Turnbull reaffirmed his support for a public vote.
But he did not criticise Senator Smith for raising the issue, or for deviating from government policy.
"Dean crossed the floor against the plebiscite bill in the Senate, you know, so he's got a long-standing view about it. But in our party, in our partyroom, members are entitled to raise whatever issues they like."
The opposition supports a vote in the parliament, where members do not have to vote along party lines.
Labor MP Terri Butler says the backbench support for gay marriage is an opportunity for the Prime Minister to get the job done.
"If there are Liberal party members and senators who are taking the time and putting the effort into drafting a bill to give effect to marriage equality in this country, then Mr Turnbull should show leadership, he should create a legacy, he should allow a free vote and he will see marriage equality pass."
Meanwhile, one backbench Liberal MP is calling for former prime minister Tony Abbott to leave politics.
It comes following a difficult period for the Turnbull Government, with Mr Abbott making frequent media appearances to criticise the government's direction and argue for more conservative policies.
Liberal MP Michelle Landry told a local newspaper it's time for Mr Abbott to leave - perhaps to take up a well-paid job as Australia's top diplomat in London.
But there's no indication that Mr Abbott wants the London job.
Victorian Liberal Party President Michael Kroger says he doesn't think the former prime minister would be interested.
And just last month, Attorney General George Brandis confirmed the current High Commissioner in London, Alexander Downer, is to have his term extended.
Senator Abetz says he'd prefer to see Mr Abbott brought into the leadership team.
"I believe that Mr Abbott should be in the cabinet. I was of the view that when Tony Abbott won the leadership, that Mr Turnbull should have been in the cabinet. That is how you develop unity and keep unity."
A cabinet reshuffle is expected later in the year.
