The previous treasurer Joe Hockey secretly proposed an increase in the GST rate from 10 per cent to 15 per cent in his last weeks in the post.

Mr Hockey was pressing the then prime minister Tony Abbott to adopt the idea as part of a sweeping reform plan, according to authoritative sources.

Mr Hockey showed Mr Abbott the Treasury modelling of the proposed changes, modelling that is now with his successor, Treasurer Scott Morrison.

The Turnbull government has been careful to keep all options for tax reform in play. It has declined to rule out an enlarged GST, despite endless goading by the Labor opposition.

The Hockey modelling, originally produced at the request of the states, informs the Turnbull government's thinking as it weighs its tax reform options.

The proposal is disclosed in part three of the Fairfax Media series Shirtfronted.

In another revelation, both John Howard and Peter Costello were urging Mr Abbott to sack Mr Hockey from the Treasury post.

Mr Howard suggested that Mr Abbott replace him with Malcolm Turnbull to reinvigorate the government and its economic narrative.

Mr Abbott rejected the advice of his mentor.

Mr Howard and Mr Costello – the duo that won the 1998 election campaigning for a GST – gave their advice to Mr Abbott separately but were united in the need for a new treasurer.

Mr Abbott was wary of Mr Turnbull's ambitions: "Turnbull doesn't want to be treasurer, he wants to be prime minister," was an Abbott phrase. Scott Morrison was another option, but Mr Abbott thought his loyalty suspect too.

Mr Abbott only decided to, in effect, offer the job to Mr Morrison in a desperate last gambit to save the government.

The Hockey tax plan was considered highly sensitive and did not go before the Abbott cabinet for debate.

The prime minister was interested in the plan but non-committal, the sources said.

"At a minimum," Mr Abbott told Fairfax Media, "we would have had modest tax cuts based on spending restraints.

"There were options for more radical reform, but whether we would have plumped for one or another would have depended on developments over the next few months, including what sort of cooperation we were going to get from the states."

Mr Hockey's proposal was designed to tax consumption more but to tax income less, the same essential concept as the Howard-Costello GST-based reform.

The extra GST, worth around $40 billion a year after it had been phased in over two to four years according to the sources, was to fund cuts to income taxes and company taxes, and pay compensation to low income earners.

The Hockey plan did not propose to expand the GST coverage beyond the existing tax base, so it would not apply to fresh food, education, health or financial services, the sources said.

This was because of the complexities in taxing financial services, and because of problems of fairness in taxing the other items.

Shirtfronted also reveals who proposed the controversial measures that became the hallmarks of the 2014 budget.

That budget was the threshold for the Abbott government's standing in the polls. Until the budget, the government was consistently ahead. Afterwards, it went permanently into a losing position.