Mr Turnbull was forced for a fourth straight day on Thursday to affirm his loyalty to the Prime Minister and support for the budget during a combative interview with Sydney radio host Alan Jones.

Mr Turnbull accused Mr Jones and conservative newspaper columnist Andrew Bolt of ''doing the Labor Party's work'' in destabilising the government.

The stoush prompted government discussion about what had fuelled the attack on Mr Turnbull, with suspicion that Jones and fellow right-wing commentator Bolt were being egged on by the hard right of the party.

Fairfax Media can also reveal that Bolt and Jones have asked Labor for ammunition to use against Mr Turnbull, particularly in relation to his stewardship of the national broadband network.

At the same time, some of Mr Turnbull's allies are privately blaming the Prime Minister's office for intervening to stop a succession of high-profile appearances on the ABC since the budget.

Bolt and Jones have both taken aim at Mr Turnbull for allegedly not selling the budget to the public, an accusation Mr Turnbull has rejected.

In a fiery morning exchange, Mr Turnbull accused Jones and Bolt of creating the furore around his alleged leadership aspirations.

Jones responded: ''There is no challenge to his leadership. They are suggesting Malcolm precisely because you have no hope ever of being the leader. You've got to get that into your head.''

Mr Turnbull replied: ''This is the most united, cohesive government we've had in this country for a long time and I think it is just very sad that you and Bolt are doing the work of the Labor Party in undermining the Abbott government.''

But questions linger over the strength of the relationship between Mr Turnbull and the Prime Minister after Fairfax Media revealed Mr Turnbull had not gone ahead with four slated appearances on the ABC.

In an interview on the ABC's 7.30 on Thursday night, Mr Turnbull said he didn't have "any plans, any desires, any expectations to be the leader" of his party again.

"Politics is an unpredictable business so people say to me often, 'Do you think you'll be leader again?' and I say my prospects are somewhere between nil and very negligible and I think that is probably about right,'' he said.

However when asked directly about his leadership ambitions, Mr Turnbull said he "didn't think there is any member of the House of Representatives who, if in the right circumstances, would not take on that responsibility".

He also said Bolt and Jones had undermined the prime minister by suggesting the government was divided which was an enormous falsehood.

"I will not stand by and let that falsehood be peddled because there is a risk if you don't stand up to bullies and people who peddle these lines, that they will start to become accepted,'' he said.

Some of Mr Turnbull's allies are privately blaming the Prime Minister's office, which vets all media appearances.

A Liberal Party source said possible changes to the ministry were behind the instability.

''There might be a few people trying to remind Abbott of their usefulness to him and loyalty when it counted [when he took over the Liberal leadership from Mr Turnbull],'' said a Liberal Party source.

Arthur Sinodinos is expected to be moved on from his suspended role as assistant treasurer after his bruising appearance at the NSW Independent Commission Against Corruption, while speculation persists that Immigration Minister Scott Morrison will step into the job of Defence Minister at the expense of David Johnston.

Parliamentary secretaries Josh Frydenberg and Steven Ciobo are considered to be two of the front runners to take Senator Sinodinos' job.