Mr Abbott, a parliamentarian for 25 years and prime minister from 2013 to 2015, said on the weekend he expected to continue in public life in some way and speculation is rife about potential posts.

Roger Corbett, a former Woolworths chief executive and the president of Mr Abbott's electorate conference in the lead-up to Saturday's election, said the outgoing MP had an "extremely good intellect" and would be offered many opportunities in his post-parliamentary life.

"It's going to be up to Scott Morrison, of course, as Prime Minister, but I do hope that Tony is offered something that's a worthwhile type of appointment," Mr Corbett said.

Liberal senator Eric Abetz, a long-time ally of the 61-year-old Mr Abbott, said it was "early days" and he would not give gratuitous advice to his former leader or Mr Morrison.

"Suffice it to say, I hope that his immense talents will be used for the benefit of the Australian people and I'm sure they will be," Senator Abetz said.

It has been suggested that Mr Abbott could fill the role of ambassador to the United States, set to be vacated by former Liberal treasurer Joe Hockey next year.

Liberal MP Craig Kelly said Mr Abbott was an obvious option to be Australia's envoy in Washington as it was a "paramount" relationship.

"You want to have someone in there with a very high stature who, if there's ever an issue, can pick up the phone and say, 'I need to speak to the President'. I think Tony would have that," Mr Kelly said.

"As an ex-prime minister, he should be given a range of options to see how he can best use his skills and talents."

Mr Kelly also suggested Mr Abbott could perform a role in Indigenous affairs, given his "deep, deep interest" in the policy area.

Soon after becoming Prime Minister, Mr Morrison appointed Mr Abbott as a special envoy for Indigenous affairs, however, many Indigenous community figures view Mr Abbott as a divisive figure.

Mr Abbott has also had a long affinity with British politics and Mr Kelly suggested another option could be Australia's high commissioner in London, a role currently held by former attorney-general George Brandis.

One source close to Mr Abbott suggested he might not be suited to an overseas diplomatic role and might prefer to stay in Australia.

"I am sure that Tony, like other former prime ministers, will continue to make a contribution to public life," Liberal senator Concetta Fierravanti-Wells said.

As an MP who entered Parliament under the old parliamentary pension system and went on to serve as a minister and prime minister, Mr Abbott will receive an annual pension of about $300,000. As a former PM, he is entitled to extra funds for office and travel expenses.

Ms Steggall, who ran on a small-l liberal platform with a climate change focus, won Warringah with an emphatic two-candidate preferred vote of 57.7 per cent. Her primary vote of 44.6 per cent topped Mr Abbott's 39 per cent, down from 51.5 per cent in 2016.

The former prime minister was viewed as increasingly out of touch with the affluent beachside electorate. He also faced concerted campaigns from local grassroots movements and national activist group GetUp.