Fairfax Media understands Liberal MPs including Dean Smith, Warren Entsch, Tim Wilson, Trent Zimmerman, Trevor Evans and Melissa Price are among those leading discussions on how to advance the issue.

The push to allow a free vote is being driven by the backbench, though some cabinet ministers are aware the discussions are underway.

The majority of the Turnbull cabinet, including Mr Turnbull, personally support same-sex marriage, but the issue has been dormant since late last year.

The argument in favour of a free vote is that Liberal MPs have historically had a conscience vote on such issues and that the position adopted under Tony Abbott, which bound MPs to support a plebiscite, was an aberration.

In November last year, Mr Wilson said in a speech that he had "discharged" his responsibility to vote for the proposed February 11 plebiscite – a vote that was defeated – and that he believed a vote could be held before the next election. Supporters believe Mr Wilson's argument is correct and they are now entitled to a free vote.

They argue that once the plebiscite date passes, and a Senate inquiry into the bill proposed by Attorney-General George Brandis is handed down in mid-February, the Liberal party room should debate the issue in the second week of the new parliamentary year, commencing February 13.

Significantly, they hope to bring the issue to a vote this year – possibly as soon as the end of March – to deal with the issue and get it off the political agenda ahead of the next election.

"No one wants this issue to go in into the May budget session, so lets deal with this quickly and relatively painlessly," one supporter of the move said.

"This could be world's biggest pain between now and the next poll."

Another MP said compromises that allow religious exemptions would be necessary and that "the feeling is that this issue won't go away, it is obstructing the government's agenda and there is now a willingness to revisit this".

"No one can have everything they want. But if the Parliament can agree on a compromise, that is a good thing."

As the backbench group agitates for change, same-sex marriage campaigners Australians for Equality will on Sunday launch a new advertising campaign across TV, newspapers and on billboards in strategic locations such as Canberra Airport, to greet MPs when they arrive on Monday for the resumption of Parliament.

Australians for Equality director Tiernan Brady said the campaign would be the biggest, most expensive one of its kind launched in Australia and focus on "changing the law to reflect Australian values".

Mr Brady said the push to legalise same-sex marriage would not go away and the ad campaign would focus on the idea that "politicians should do their jobs" and vote on the issue.

"Australians are for marriage equality," he said. "They are not unsure, they are not a little in favour, it's 65 per cent-plus in favour. Australia is in the top 10 countries in the world in favour of marriage equality."

Some Liberal Party MPs Fairfax Media has spoken to who oppose legalising same-sex marriage believe the law change is inevitable and that it may be time for the change to happen via a free vote given the issue sucks up oxygen and distracts from the Coalition's core agenda.

If a free vote was allowed for Liberal Party MPs, it is likely the laws would be passed with the support of Labor, the Greens and crossbench MPs. It would see Australia join other anglophone countries including the United States, Britain, New Zealand, Canada and Ireland in allowing the unions.

But other more conservative MPs would fight tooth and nail to stop any fresh push and warned a civil war could erupt if Mr Turnbull did not stop the push.

Another complication is the Coalition agreement between the Liberal Party and Nationals specifies that a plebiscite be held, suggesting any attempt to engineer a free vote could set off a brawl between the two governing parties.

As recently as December, Mr Turnbull said the plebiscite remained Coalition policy and insisted it was the mechanism by which same-sex marriage could become reality.

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