Turnbull says cabinet will be announced Monday, amid reports Dutton has offered resignation

Immigration minister Peter Dutton has offered his resignation to newly appointed Prime Minister Malcolm Turnbull, according to reports.

Sky News reported that Mr Dutton, who stood in support of Tony Abbott during Monday's leadership ballot, offered his resignation via text message.

Mr Turnbull is reportedly yet to accept the offer.

When asked about the reports this morning, the prime minister said he had not met with Mr Dutton today.

Mr Dutton was in the spotlight last week after he was recorded on a microphone making a joke about the impact of rising seas on Pacific Islands.

"Time doesn't mean anything when you're about to ... have water lapping at your door," he was heard saying.

At his first press conference since becoming prime minister, Mr Turnbull today confirmed his new-look cabinet would be sworn in on Monday.

There is speculation that assistant immigration minister Michaelia Cash could take the role as immigration minister.

The roles of a number of ministers, including Treasurer Joe Hockey and Minister of Defence Kevin Andrews, are under scrutiny now that Mr Turnbull has replaced Mr Abbott.

Mr Turnbull said he had spoken to Mr Abbott but was not aware of his intentions going forward.

Mr Hockey this morning refused to speculate on whether he would retain his position next week.

He said he had sworn on the Bible to the Governor General he would do his job, and that right now that meant helping Australians get a job.

There is widespread speculation Mr Hockey could be replaced as treasurer by Scott Morrison.

READ MORE: Hockey maintains he'll always remain loyal to party leader