Senior government minister Peter Dutton has refused to reject reports he offered his resignation to Prime Minister Malcolm Turnbull after singing the praises of Tony Abbott before Monday night's leadership spill.

Reports emerged on Wednesday that Mr Dutton, who holds the contentious Immigration and Border Protection portfolio, had volunteered to quit in a text message sent to Mr Turnbull. However he also reportedly offered to stay on and serve if needed.

It is understood the resignation offer has not yet been accepted.

A spokeswoman for Mr Dutton would not confirm or deny the claim, saying: "We don't have any comment to make on that".

Labor MP Andrew Leigh raised the claims in Parliament on Wednesday, which Mr Dutton dismissed as a "juvenile interjection".

Ahead of the ballot on Monday, Mr Dutton said Mr Abbott was a "decent person" who could beat Labor leader Bill Shorten at the next election.

He said the base of the party was to the right of centre on many issues and Mr Abbott was best placed to represent the members.

Mr Dutton predicted Mr Abbott would win the ballot.

Asked if Foreign Affairs Minister Julie Bishop had been a loyal deputy, he replied: "That's a question for her to answer."

Mr Turnbull's office would not comment on the resignation offer. At a press conference on Wednesday he refused to discuss the final composition of his cabinet, saying only "I expect the new ministry, with some changes, to be sworn in on Monday".

Mr Turnbull said he was "very committed" to seeing more women in cabinet.

There has been speculation Liberal MP Michaelia Cash would take on the immigration portfolio. She is currently the Assistant Minister for Immigration and Border Protection.

Mr Dutton's gaffe late last week, in which he joked about the effect of rising seas on Pacific Islands, overshadowed what should have been a triumphant week for the Abbott government.

Mr Abbott, who lost the prime ministership to Mr Turnbull on Monday, was praised last week after announcing Australia would accept 12,000 refugees fleeing war-torn Syria.

Mr Dutton had been dispatched to Geneva earlier in the week to discuss Australia's assistance with the UN's refugee agency, the UNHCR. On the way home, he visited Cambodia to salvage Australia's $55 million agreement to resettle refugees from Nauru in the impoverished nation.

However, on Friday Mr Dutton embarrassed the government when a microphone picked up his joke about punctuality at a recent meeting of Pacific Island leaders, when he said "time doesn't mean anything when you're about to ... have water lapping at your door".

He was later forced to apologise after Pacific Island leaders described the joke as "vulgar" and insensitive to the plight of those whose homes face inundation.

Mr Dutton has weathered constant salvos from critics in the immigration portfolio, as he implemented the government's tough border protection and asylum seeker policies.

However, supporters have praised his efforts in helping stop the flow of asylum seekers arriving in Australia by boat.

Last month, Mr Dutton was drawn into the Australian Border Force fiasco in Melbourne, in which a police operation was aborted after a press release suggested random visa checks would be conducted.

The press release was sent to Mr Dutton's office as an attachment to a briefing note about the operation, but was not opened because it appeared "routine".

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