The Federal Government is considering bankrolling the opponents and supporters of gay marriage ahead of a plebiscite on the issue.

The Government has vowed to hold a national vote on whether to legalise same-sex marriage, if elected.

Attorney-General George Brandis has been giving evidence in Senate estimates and said funding was still being considered.

"The question of funding of the yes or no case is under consideration and it's not a matter on which a decision has been made," Senator Brandis said.

"Were there to be allocation of public money, of course both sides of the argument would be entitled to equal treatment."

Greens senator Robert Simms asked whether the Australian Christian Lobby (ACL) could be given funding for the "no" campaign.

"In the event there were to be public funding, then on behalf of both the 'yes' and the 'no' case, there would have to be an entity or a structure representative of that point of view who was accepted by the stakeholders," he said.

The ACL has previously called for the Government to suspend anti-discrimination laws during any plebiscite campaign.

But Attorney-General Brandis today rejected such a move.

Prime Minister Malcolm Turnbull has vowed to push ahead with a plebiscite, following debate in the Coalition partyroom last year.

The Federal Opposition and the Greens say the issue should be resolved by a vote in Parliament, instead.

Attorney-General Brandis has previously said the Government planned to hold the vote before the end of the year.