Senator Dean Smith plans to take a bill for same-sex marriage to the Liberal party room in a push to get the government to abandon its plebiscite and conduct a free vote before the end of the year.

Smith, a Liberal senator for Western Australia, told The Sunday Times that he was working on a private member's bill that he will take to the party room in the near future.

“I don’t doubt the complexity same-sex-marriage presents for some Liberals, but I am not asking people to change their mind on the issue," Smith told the Perth newspaper.

“Instead, we should allow everyone the right to vote according to their own conscience. The coalition’s position is clear – a plebiscite – so people should not underestimate the challenge of securing a free vote on the issue.

"Many [Australians] do support the matter being put before the parliament and finally resolved. The time is now."

Smith's announcement comes two weeks after cabinet minister Christopher Pyne said to a meeting of Liberal moderates that same-sex marriage may come "sooner than everyone thinks".

In response to the commotion over Pyne's comments, prime minister Malcolm Turnbull repeatedly pledged that the government will not budge from its current position of a national vote on same-sex marriage.

If this remains the case, a same-sex marriage bill could only pass the House of Representatives if government MPs cross the floor to team up with Labor and the cross bench to suspend standing orders and force a vote.

You can read an explainer of what exactly would need to happen here.