Two Liberal MPs have been secretly working on a plan to legalise same-sex marriage in Australia as soon as August, with a draft copy of the laws well advanced and consultation with advocates under way.

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.