A series of key portfolios will remain in the same hands, but a set of retiring ministers means he has gaps to fill.

Ken Wyatt is tipped to take on indigenous affairs, becoming the first indigenous Australian to hold the role.

"I'll just take on board whatever the prime minister determines for me," Mr Wyatt told Sky News on Tuesday.

"What I want to do is make a contribution to a common sense approach across a number of areas in our country."

Labor was planning to appoint "father of reconciliation" Patrick Dodson to the role if the party won the election, but the Liberals now have the chance to make history.

Western Australian MP Ben Morton travelled with Mr Morrison for the election campaign and looks set for a promotion, while assistant defence minister David Fawcett could also take a step up.

West Australian senator Linda Reynolds has already been promised the Defence portfolio to replace Christopher Pyne.

Mr Morrison will have to find new ministers for industrial relations, jobs, women, and human services.

Others talked about for promotions include WA MP Steve Irons, and Victorians Tim Wilson and Jane Hume.

Environment Minister Melissa Price is facing pressure to keep her role after struggling to answer questions. She has rarely been allowed to do press conferences on her own since taking over the job in August.

"Anyone but Melissa Price would do a better job," Greens leader Richard Di Natale told reporters in Melbourne.

"You know what would be nice? An environment minister who cared about the environment."

Tasmania contributed an extra senator and two extra lower house seats to the coalition win, leading some to expect more key positions in line with previous good results in the Apple Isle in 2004 and 2013.

If so, the prime minister will have to choose between veteran Eric Abetz and younger senator Jonathon Duniam, as well as consider whether to promote Richard Colbeck into cabinet.

Peter Dutton is expected to keep Home Affairs, while Treasurer Josh Frydenberg and Finance Minister Mathias Cormann are also set to stay in the same roles.

Attorney-General Christian Porter will be Leader of the House, replacing Mr Pyne in the job of managing the day to day of parliament tactics.

Health Minister Greg Hunt, Education Minister Dan Tehan and Foreign Minister Marise Payne are likely to keep their spots.

The new ministry is not expected to be announced until at least this weekend, as counting continues following Saturday's election.

Australian Associated Press