But the push to establish the scheme will not head off a push led by Nationals senator Barry O'Sullivan to set up a wide-ranging banking commission of inquiry, which is similar to a royal commission but reports to Parliament, not the executive.

Treasurer Scott Morrison and Financial Services Minister Kelly O'Dwyer has been working on the scheme for some time and Mr Morrison this week held high-level discussions with the heads of Australia's major banks about signing up to the scheme, which has been discussed by the cabinet.

A panel or tribunal would be created to review so-called legacy cases and consider claims for financial compensation from victims, with a compensation fund set up that banks would contribute to.

Government insiders have told Fairfax Media the scheme could be unveiled as soon as next week, though they stressed key details of the scheme have not been finalised.

A spokesman for Senator O'Sullivan said "there will be no change to our plans". The bill is likely to sail through the Senate with Labor and Greens support but the powerbroker needs two of his colleagues in the lower house to cross the floor and team up with the opposition and crossbench to facilitate its passage.

Mr Morrison hinted on Thursday at the plan to address so-called legacy cases in which people have been ripped off, but have not been able to secure compensation.

"For some years now I've been talking to the banks about resolving some legacy cases where people have had issues. These cases have been raised in various fora. I've been impressing upon them for some time now the need for those cases to be resolved and, like in other meetings I've had with them, I'll continue to have those discussions as well as on other matters," he said.

One of the major grievances cited by government MPs such as Mr O'Sullivan - and other Coalition MPs such as Warren Entsch and George Christensen - is that people or businesses with so-called legacy cases do not have a clear course to pursue to secure compensation for being ripped off.

The scheme would be separate from the government's already-announced Australian Financial Complaints Authority, which are from the Ramsay review of Australia's external dispute resolution and complaints framework, and which is designed to deal with future cases of banks bad behaviour.

The Nationals' revolt over the banks, and the push for a commission of inquiry, comes as Queensland goes to the polls on Saturday, with One Nation poised to strike deep into the junior Coalition partner's regional heartland.

A note sent by Citigroup on Friday morning suggested the last resort compensation scheme was a "compromise solution to head off a banking royal commission".

"Under the proposed arrangement, the federal government would establish an independent panel of legal experts to investigate claims of bank misconduct. The panel would need to be able to provide legal protections for customers, staff and whistleblowers, which the Parliament is currently unable to offer."

It incorrectly suggested compensation could be funded by a small increase in the government's big bank levy and added that the big banks "may reject the government's proposal as they may form the view that they will get a royal commission under a Labor government in any case".

Senator O'Sullivan's inquiry would have three commissioners appointed by the Senate to run what will initially be a one year inquiry.

One would be a former judge, one a banking and financial services expert, and one would be a community representative.

The inquiry will examine unethical or unlawful conduct by banks, insurance, superannuation and financial services companies, the regulatory system, agencies and laws that governs them, and whether a better dispute resolution system could be established to help consumers.