Fairfax Media can reveal WA senator Dean Smith and NSW lower house MP Trent Zimmerman are working on a private members' bill they hope will be presented to Parliament to legalise same-sex marriage through a conscience vote, rather than the Turnbull government's stated policy of a national, non-binding plebiscite.

It's understood cabinet ministers Christopher Pyne and George Brandis - both of whom support same-sex marriage - are aware of the existence of the bill, which is designed to end the political impasse over the issue and get it off the political agenda before the next federal election.

Senator Smith and Mr Zimmerman have been consulting with the director of legal advocacy at Melbourne's Human Rights Law Centre, Anna Brown, who is also the co-chair of Australians for Equality, on the details of the legislation.

In keeping with the recommendations of a February Senate committee report, the draft bill would allow exemptions for religious and other celebrants who did not wish to marry two people of the same sex.

While the bill is unlikely to be selected for debate by the government-controlled parliamentary committee that chooses bills, it would take only a handful of Liberal MPs to side with the opposition and crossbench, reach an absolute majority of 76 votes and force the law to be considered.

Once that happens, Liberal MPs who support same-sex marriage could team up with Labor and the crossbench on the floor of Parliament to legalise same-sex marriage.

The bill would almost certainly then sail through the Senate with the support of Labor, the Greens, the crossbench and some Liberal senators.

Senator Smith was unavailable for comment because he is travelling, while Mr Zimmerman and Ms Brown declined to comment when contacted by Fairfax Media. Senator Brandis and Mr Pyne were also contacted for comment.

In a statement, Mr Pyne said "the government has no plans to alter the policy".

However, in an interview with Huffington Post Australia, Senator Smith said there was a "natural symmetry" about having a free vote in Parliament on the two-year anniversary of government adopting its now-defeated plebiscite policy in August.

Liberal moderates are frustrated by the lack of action on same-sex marriage following the defeat of the plebiscite earlier this year, and believe Prime Minister Malcolm Turnbull should stand up to the conservative wing of the Liberal Party and allow a free vote on the floor of the parliament.

However, Mr Turnbull will face pressure from the conservative wing of his party not to allow a free vote to occur.

Mr Turnbull - who personally supports same-sex marriage but is concerned about keeping the conservative wing of his party onside - said on Monday his government's position of a non-binding national plebiscite on the matter was clear and that "we have no plans to change it, full stop".

Those comments were made after a leaked audio recording of Mr Pyne emerged on Monday, in which the Leader of the House predicted same-sex marriage could be legalised "sooner than everyone thinks".

Mr Pyne's remarks were made at a gathering of Liberal moderates on Friday night in Sydney as the Liberal federal council met. The recording was leaked to conservative News Corp columnist Andrew Bolt.

He told the gathering of moderates that "we [Liberal moderates] are in the winner's circle but we have to deliver a couple of things and one of those we've got to deliver before too long is marriage equality in this country".

"Your friends in Canberra are working on that outcome."

That leak prompted former prime minister Tony Abbott, who introduced the plebiscite policy nearly two years ago, to accuse Mr Pyne of not being fair dinkum and suggesting he was disloyal to the government.

"To dump the plebiscite, to do anything without a plebiscite would be a breach of faith with the people," Mr Abbott told radio station 2GB.

- with Fergus Hunter