Prime Minister Tony Abbott says the Speaker Bronwyn Bishop did the "right thing" by handing in her resignation, and choosing a successor will ultimately fall to the Coalition party room to decide.

The veteran Liberal MP resigned from the Speaker's chair in disgrace on Sunday, after weeks of intense pressure over questionable travel entitlements claims.

"Bronwyn did the right thing [on Sunday]," Mr Abbott told reporters in Adelaide.

"Obviously she had done the wrong thing on a number of previous occasions."

The ABC understands a new speaker will be nominated at a Government party room meeting next Monday morning when Parliament resumes after the winter break.

The selection would need to be endorsed by the House of Representatives, but the Coalition's majority means the Government has the power to decide who will take the speaker's chair.

A number of contenders are jockeying for the position.

Nationals MP Bruce Scott is the deputy speaker but is not considered a likely prospect.

Two Liberal MPs have already expressed an interest in the role; the longest serving member or "Father of the House" Philip Ruddock and Victorian backbencher Russell Broadbent.

Discussions are also underway among Liberal MPs about the possible candidacy of Melbourne-based Tony Smith and Andrew Southcott from Adelaide.

Federal Member for Murray Sharman Stone announced she would not be contesting the position.

Chair choices 1. Philip Ruddock: "Father of the House", former immigration minister in the Howard government, former Abbott Government whip. 2. Tony Smith: Victorian backbencher and chair of the closely watched electoral matters committee. 3. Andrew Southcott: South Australian backbencher. 4. Russell Broadbent: Victorian backbencher. 5. Ross Vasta: Queensland Liberal National Party MP

"Despite speculation, I will not be a contender for the position of speaker in what I hope will be a party room vote next week," she said.

Ms Stone said she would continue to speak out on behalf of her electorate, adding "A speaker does not have these same avenues for advocacy".

Labor has linked Mrs Bishop's demise to the Prime Minister's judgement, arguing she was a "captain's pick" chosen by Mr Abbott.

But Mr Abbott told reporters in Adelaide the election of the speaker was "always a matter for the party room".

"Sometimes there's only one nomination," he said in reference to Mrs Bishop's appointment in 2013.

"The party room will choose a nominee and obviously the Government's nominee then goes before the Parliament and the Parliament ultimately determines who the speaker will be."

"I'm confident there will be quite a number of good people who will indicate some interest in the job and then it will be up to the party room to make a decision," Mr Abbott said.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 6 minutes 30 seconds 6 m Entitlements for politicians will be subject to a 'root and branch inquiry' according to Special Minister of State Senator Michael Ronaldson.

He also suggested consensus could build ahead of the party room meeting, meaning only one candidate would formally nominate for the role.

Despite those protestations there are Government MPs who would prefer Mr Abbott made the final decision.

Queensland backbenchers Andrew Laming and Ewen Jones said they would both support the Prime Minister picking the replacement speaker himself.

Mr Abbott stressed Mrs Bishop's decision to resign was "unprompted" and rejected the suggestion from reporters that the 72-year-old had been offered another job in exchange for standing down.

"There has been no offer," he said.

Mr Abbott has promised a "root and branch" review of the entitlements system in response to the controversy.

Special Minister of State Michael Ronaldson said a review of parliamentary entitlements was needed to restore public faith in the system.

He pointed to entitlements already wound back by the Government and said it needed to go further.

"Clearly more needs to be done, and that's exactly what we will be doing," he said.

"It will take time, it will involve the community, undoubtedly it will involve some of my colleagues who want to have some submissions, but we need to get this sorted out and restore public faith in the system."