Tony Abbott insists Bronwyn Bishop's decision to quit as Speaker of federal parliament was "unprompted".
The prime minister also rejected suggestions Mrs Bishop had been offered any incentive to end the expenses scandal that has dogged the government since mid-July.
"There has been no offer," Mr Abbott told reporters in Adelaide, where cabinet will meet on Tuesday, acknowledging he'd had a number of conversations with Mrs Bishop in recent days.
"Bronwyn came to the right decision ... and while she obviously had done the wrong thing in a number of significant respects, she abundantly did the right thing (in resigning)."
South Australian MP Andrew Southcott appears to be firming as favourite to take on the vacant post when the coalition party room meets in Canberra next Monday.
Dr Southcott says he has "consulted with colleagues" and will be offering himself as a candidate.
"It is one of the most important roles in federal parliament and I would be honoured to serve if asked to do so," he said in statement.
But veteran Liberal and former minister Philip Ruddock, who confirmed his interest in the role, is also considered a chance.
Opposition Leader Bill Shorten, who recommended Deputy Speaker Bruce Scott and Liberal MP Sharman Stone, said he hoped Mr Abbott did not impose another "captain's pick" on the parliament.
"If it's Mr Scott or indeed if it's Sharman Stone from the seat of Murray, they are both people who at least don't have the same hyper-partisanship which has really made the last 21 months of Mr Abbott's government and the parliament such a laughing stock," he told reporters in Melbourne.
Cabinet minister Andrew Robb is open to the idea of the next Speaker withdrawing from the party room.
"It is important that there's a significant measure of independence," Mr Robb said.
Mr Abbott has ordered a review of entitlements headed by former Finance Department secretary David Tune.
While the review was welcome, Mr Shorten said it would take a "different mode of behaviour" to fix the problem.
Communications Minister Malcolm Turnbull said the entitlements system was stuck "very much in the last century" and the use of smartphone apps could make MPs instantly accountable.
"The most important thing is that it is taxpayers' money and to use it responsibly and prudently," he said.
The Finance Department is examining 10 years of Mrs Bishop's expenses claims, including a $5200 helicopter charter in 2014, which could be referred to the Australian Federal Police if any possible criminality is identified.
Mr Abbott said the public wanted to have confidence MPs were working for them and "not simply off on frolics of their own".
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