Evidence is emerging that new Prime Minister Malcolm Turnbull is setting about arranging his new frontbench.

There has been much speculation about the future of the Treasurer Joe Hockey, who was seen as the target of Mr Turnbull's economic criticism ahead of his moves to overthrow Tony Abbott.

Mr Turnbull's office has said the reshuffle is likely to be announced over the weekend or early next week, and a ministerial meeting was held last night.

The ABC's Barrie Cassidy said he had been told the Social Services Minister Scott Morrison has been offered the position of Treasurer.

According to his information, Mr Hockey has been offered the chance to remain in Cabinet, and is likely to be offered the Communications portfolio.

Mr Hockey called a media conference on introduction of multinational anti-avoidance legislation, and refused to go into the details of his private conversations with Mr Turnbull.

"I've had discussions with the Prime Minister," he told reporters in Canberra.

"We'll leave it at that. We'll see what happens."

The ABC has confirmed Immigration Minister Peter Dutton offered his resignation to Mr Turnbull in a text message on Monday night, but he also offered to stay and serve.

Mr Turnbull said today he had not spoken to Mr Dutton.

Michaelia Cash is likely to be promoted to Immigration and Arthur Sinodinos to employment.

Ministers push to remain in their jobs

A number of senior ministers are pitching to remain in their portfolios ahead of the Cabinet reshuffle.

Mr Turnbull has told Parliament he is sticking with climate change targets settled under the former prime minister.

Environment Minister Greg Hunt said he was feeling comfortable but taking nothing for granted with his portfolio.

"Optimistic but never to be presumptive," Mr Hunt told ABC local radio.

"I am actually very, very comfortable with circumstances because what we see is that the fundamental policy has been embraced."

Defence Minister Kevin Andrews is pushing to remain in his job.

"I think that continuity at the moment is quite important in this instance," he said as he confirmed Australia has conducted its first air strike in Syria.

"We're operating this mission in Iraq and Syria, we still have forces in Afghanistan, we're virtually weeks away from the publication of the Defence White Paper."

Finance Minister Mathias Cormann has called on colleagues to rally round Mr Turnbull.

"I look forward in the months and years ahead to work with Prime Minister Turnbull to do everything I can to help put Australia on a stronger foundation for the future."