Veteran Liberal MP Philip Ruddock has expressed his interest in replacing Bronwyn Bishop as the speaker of the House of Representatives.

Mrs Bishop resigned from the position yesterday afternoon following sustained pressure over her travel expenses.

She had faced fierce criticism for almost three weeks since it was first revealed she spent more than $5,000 chartering a helicopter from Melbourne to Geelong to attend a Liberal Party fundraiser last November.

Coalition MPs the ABC has spoken to believe "Father of the House" Mr Ruddock, 72, is the most likely replacement for Mrs Bishop.

Mr Ruddock's office released a statement saying he would be available if his parliamentary colleagues sought it.

He made headlines earlier in the year when he was sacked as chief government whip after Prime Minister Tony Abbott indicated Mr Ruddock "wasn't as aware as he should have been" of backbench unrest over his leadership.

Nationals MP and deputy speaker Bruce Scott has not said publicly whether he wants the job, but it is understood he could also be a candidate.

However, it is felt the Liberals would not want to give such a prized job to a Nationals MP unless a deal was cut involving the Nationals giving up a ministerial role.

One Nationals MP said there was no way the party would give up a frontbench role, therefore likely ruling Mr Scott out of contention.

But Deputy Nationals leader Barnaby Joyce said Mr Scott would be a good choice.

"Because he has the capacity just to deal with that role, he's retiring himself so no-one needs to feel threatened," he said.

"There's still going to be the job for the speaker there after the next election and if somebody wanted a stop-gap between now and the election, then I think Bruce Scott would be an obvious choice."

Opposition Leader Bill Shorten said Mrs Bishop was appallingly biased and voiced his support for Mr Scott.

"I hope that person does not attend the party room, I actually think it should be Bruce Scott from the National Party," he said.

"Now it may sound odd a Labor guy proposing that someone from another party should get a go, but I think Bruce Scott's sufficiently unpartisan," he said.

Cabinet Minister Andrew Robb said there was "some merit" in Mr Shorten's contention that the speaker should not attend party room meetings.

"We'll talk it through. It is important that there's a significant measure of independence," he said.

Mr Scott was first elected to represent the electorate of Maranoa in the House of Representatives in 1990, and has been deputy speaker since 2012.

He announced yesterday he will not contest the seat at the next election.

Victorian Liberal Russell Broadbent is another name mentioned as a possible speaker and confirmed he would take the role if he had Mr Abbott's support.

A moderate on social issues, Mr Broadbent is viewed as having a good relationship with Labor and is a member of the speaker's panel, meaning he can act in the role of deputy speaker.

Many in the Coalition party room were unhappy with the way Mrs Bishop was presented to them as a "captain's pick" for the speakership.

This time they want a role in picking her replacement.

Communications Minister Malcolm Turnbull said he "assumed" they would get one.

"There are a lot of members who would ... do the job very well, but that I assume will be a matter for the party room in due course," he said.

Another Victorian Liberal, Sharman Stone, was also suggested as a potential candidate but none of the MPs canvassed by the ABC expected she would get the job, citing her public clashes with the Prime Minister over his leadership.

Dr Stone said being speaker would limit her ability to advocate for changes in her own electorate.

"I'd have to think very, very seriously about it and I actually do think it shouldn't be a matter of the job being offered — it should be a matter of the party room voting on the candidates they think could do the job well," she said.

Bruce Scott has been deputy speaker of the House of Representatives since 2012. ( AAP: Lukas Coch )

South Australian Liberal MP Andrew Southcott has also been mentioned as a possible candidate and said he would be canvassing his colleagues for support.

"I'm flattered to see my name put forward," he said.

"Ultimately it's a decision of the Parliament and I'll be speaking to my colleagues this week."

There was speculation among Liberal and Nationals MPs that the Defence Minister Kevin Andrews may be asked to take on the role, but it is understood he has said he does not want to give up his Cabinet position.

It was felt this option was also unlikely because it would require a frontbench reshuffle, which MPs did not believe the Prime Minister wanted to embark on.

Mrs Bishop cannot be replaced until Parliament resumes next Monday, as the appointment of the position of speaker is through a vote of the Lower House.

Bishop should not be 'let off the hook'

Federal MPs have welcomed the Prime Minister's review of politicians' entitlements in response to the Bishop travel controversy.

Mr Turnbull said a review was a good idea but MPs need to apply common sense.

"This is always going to depend on spending the taxpayers' money in a prudent way," he told Radio National this morning.

Labor MP Pat Conroy also welcomed the review but said Mrs Bishop still needed to be made accountable.

"We shouldn't let Mrs Bishop or Tony Abbott off the hook on this," he said.

Former speaker and Labor backbencher Anna Burke agreed the system of entitlements needed to be reviewed, but also rejected Mr Abbott's view the problem was with the system, not the person.

"It's not about entitlements, it's about people's interpretation of them," she told 774 ABC Melbourne.

"Bronwyn Bishop resigned because of her failings in her understanding of what is right and wrong.

"No other person would've thought it was reasonable to hire a helicopter, that it was within our entitlements to hire a helicopter down to a Liberal Party fundraiser."

Ms Burke says she supports the idea of having an independent arbitrator for entitlements like they do in the United Kingdom.

"I don't know that you would want to go the full IBAC [Independent Broad-based Anti-corruption Commission] route, but maybe there is something in between like having in independent arbitrator having a look at that," she said.

The Finance Department is continuing to investigate Mrs Bishop's use of chartered flights and other entitlements claims dating back a decade.

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