Liberal Democrat David Leyonhjelm is poised to introduce his long-awaited same-sex marriage bill to the Senate, in a move that will increase the pressure on the Liberal Party to allow its MPs a conscience vote on the issue.

Senator Leyonhjelm is due to introduce his Freedom to Marry Bill to the upper house on Wednesday afternoon, which would allow gay, transgender and intersex people to marry.

Liberal Democrat senator David Leyonhjelm Credit:James Alcock

He will flag his plans in a speech to the Senate on Tuesday evening.

The bill proposes to change the wording of the Marriage Act to define marriage as "the union of two people" rather than a "man and a woman". But it will not make it compulsory for celebrants to marry same-sex couples, except in the case of government employed celebrants.