Following his sudden ouster as Australia's prime minister three months ago, Mr Tony Abbott insisted there would be "no undermining" of Mr Malcolm Turnbull, the man who replaced him.

But many observers now believe Mr Abbott has been doing exactly that since losing the leadership in a surprise Liberal Party-room vote.

Mr Abbott and his uncertain future have been a constant distraction for the Turnbull government.

He has regularly emerged to make bold public statements - particularly on national security - which have attracted headlines and cemented his reputation as a conservative figurehead, in stark contrast to Mr Turnbull's reputation as a progressive.

Earlier this month, he controversially declared that Islam needed to undergo a religious "reformation" and urged the West to "be ready to proclaim the clear superiority of our culture to one that justifies killing people in the name of God".

"We can't remain in denial about the massive problem within Islam," he wrote in Sydney's Daily Telegraph.

Mr Abbott has yet to declare whether he will stand for election as an MP at the next polls, due next year. But he has hinted that he wants to stay in Parliament, saying he believes he will win the next election.

"I've had thousands and thousands of messages of encouragement since mid-September," he told Sky News earlier this month. "The message I'm getting is I still have a contribution to make to public life."

But an opinion poll published last Saturday indicated that voters are not particularly enthralled by the possibility of the staunch conservative remaining in politics.

The survey in his Sydney electorate by ReachTel polling found that 51 per cent wanted him to retire, 35 per cent wanted him to stay and the remainder were undecided.

The quandary facing Mr Abbott - the third successive sitting premier to be deposed - has become all too familiar in Australian politics.

He can choose the path of Mr Kevin Rudd, who was dumped as prime minister in 2010 and clawed his way back to the job but caused three years of Labor leadership instability. Or he can choose the path of Ms Julia Gillard, who was ousted by Mr Rudd in 2013 and declared she would resign from Parliament to ensure a smooth succession.

Analysts believe Mr Abbott's choice will significantly affect the fate of Mr Turnbull and his ruling coalition ahead of the next election.

Mr Turnbull, a 61-year-old former investment banker, holds far more progressive views than Mr Abbott, particularly on issues such as combating climate change, same-sex marriage and whether Australia should abandon the British monarchy to become a republic.

Despite being far more publicly popular, Mr Turnbull is mistrusted by the more conservative members of his party who largely prefer Mr Abbott, also a devout Catholic.

Political commentator Laura Tingle last Wednesday said Mr Turnbull risks damaging his strong appeal as a centrist candidate if he is forced by Mr Abbott to continually placate the party's conservatives.

Since taking office, Mr Turnbull has already restrained his personal support for a carbon emissions trading scheme and for a free vote of MPs on same-sex marriage.

"With the Prime Minister having to look over his right shoulder to a disgruntled former prime minister, his capacity to both appeal to and redefine the centre of Australian politics is more limited," Ms Tingle wrote in The Australian Financial Review.

"It is Turnbull's appeal to that centre which makes him so politically powerful; many Labor voters see him as their ideal prime minister. If Abbott can interfere with that message, he will help damage Turnbull - and his own government's fortunes."

Many commentators believe Mr Abbott will never be prime minister again because of his personal unpopularity and his poor leadership style. He lost the support of his fellow MPs after slumping in the polls and making some contentious decisions, including his much-ridiculed move to award an Australian knighthood to the husband of Britain's Queen Elizabeth.

But his backers think differently.

MP Eric Abetz has called on the former leader to remain in politics and to vie for - at least - a Cabinet position.

"I think he (Abbott) would be well suited to serve in a range of portfolios but, importantly, I think the conservative voice deserves stronger representation around the Cabinet table," he told The Saturday Paper.

Asked whether Mr Abbott could return as prime minister, he said: "In politics, you never say never."