Cabinet minister Peter Dutton has reportedly proposed a “voluntary postal vote” to settle Australia’s stance on same-sex marriage.

Mr Dutton is believed to be working behind-the-scenes for an alternative path which could see gay marriage legalised in Australia, according to Fairfax Media reports.

An investigation revealed he and fellow cabinet minister Mathias Cormann, both openly opposed to same-sex marriage, are pushing for a postal plebiscite to be held before the matter goes to a parliamentary vote.

This comes one week after Mr Dutton criticised corporate leaders including Qantas chief Alan Joyce for publicly supporting marriage equality, telling them to “stick to their knitting”.

A postal vote would not require legislation, would give citizens the option to opt out of voting, and save significant expenses.

But Prime Minister Malcolm Turnbull is understood to be “wary” of the concept.

When asked about his stance on the alternative in Canberra on Wednesday, Mr Turnbull did not give anything away.

“We went to the election with a policy for a plebiscite which would give every Australian a say,” he said.

“Our position is very clear. We want to give all Australians a say on the matter.”

He said that if the plebiscite had not been rejected by the Senate, the issue would have already been settled.

In a speech in Canberra on Wednesday afternoon, senior cabinet minister Arthur Sinodinos said he would like to see same sex marriage settled in this parliamentary term.

Fairfax Media reported that, while speaking privately, Mr Dutton has said it was inevitable that same-sex marriage would become law in Australia, so it would be preferred that the Coalition, rather than Labor, controlled the process.

Some Liberal ministers recognise that a victory on same-sex marriage would enhance the Prime Minister’s standing with voters, while other conservatives want to delay action on the matter.

Australian Marriage Equality chair Alex Greenwich said the proposal was a “desperate ploy” that would be a “pretty sneaky and underhanded way” to finalise the issue.

A spokesman for Mr Dutton said he remained committed to a plebiscite on same-sex marriage.

In a Linkedin post on Tuesday, Qantas chief Mr Joyce said business bosses “absolutely should” speak out about marriage equality.

“Polls show that’s also what the majority of the Australian community believes – people who are our shareholders, customers and employees,” he said.

“So, we’re comfortable with our position and on speaking out about it.”

– With AAP.