Protections against discrimination for gay students in religious schools could become law before the end of the year.
The chances of the coalition government and Labor striking a deal received a boost on Tuesday, when senators agreed to vote on legislation by Wednesday afternoon.
Government Senate leader Mathias Cormann said Prime Minister Scott Morrison had reached out to Labor leader Bill Shorten to find a reasonable compromise forward on the issue.
Senators are due to debate the Labor bill for a little more than 90 minutes on Wednesday before voting.
"We look forward to genuine and good faith engagement with the opposition, but also with others in the parliament, in the intervening period," Senator Cormann told parliament on Tuesday.
The coalition has argued the legislation needs to be refined to give schools the right to conduct themselves in a way reasonably in line with their faith.
There is agreement across the political divide that the Sex Discrimination Act needs to be updated to remove religious schools' right to exclude students based on their sexuality.
Mr Morrison and Mr Shorten have both said they wanted the matter addressed before parliament rises for the year on Thursday.
