Coalition MPs are working on draft laws to set up a commission of inquiry into the banks, which Prime Minister Malcolm Turnbull continues to resist.
Queensland Liberal National Party senator Barry O'Sullivan, who is behind the new push, expects to circulate the bill next week ahead of parliament's return on November 27.
Senator O'Sullivan said the commission of inquiry would be identical to a royal commission in terms of its power and reach, but would report to the parliament.
If it passes, the government would then need to decide whether to fund it.
The inquiry replicates a number of previous attempts to get a banking probe up and running.
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"I'm in the process of blending the (previous) bills so that I hope I can get one suitable to all colleagues in the Senate," Senator O'Sullivan told AAP on Friday.
"That will increase its chances of success."
Senator O'Sullivan said he would not press ahead with the bill until the same-sex marriage legislation was passed by the Senate.
He said the marriage laws, introduced by Liberal senator Dean Smith, provided a model in terms of backbenchers seeking cross-party support to tackle issues of importance to the Australian community.
"We'll follow Dean Smith's footprints. He pioneered a way to get backbench bills through."
Mr Turnbull said the government had made "enormous reforms" in the banking and financial sector and another inquiry was not needed.
"We're seeing much greater accountability ... we've given more money and more teeth to the regulators, including ASIC and APRA and we're ensuring that people have a streamlined way of dealing with complaints," Mr Turnbull said.
A Greens bill setting up a bank commission of inquiry passed the Senate earlier this year but narrowly failed to get through the lower house.
However, Senator O'Sullivan has higher hopes of his bill getting through both houses.
