Labor will seek on Thursday to give a government senator an opening to introduce a bill setting up a commission of inquiry into the banks.
Liberal National Party senator Barry O'Sullivan has been in discussions all week with coalition colleagues, Labor and the Greens on a bill to set up an inquiry into the banking, superannuation, insurance and financial services sector.
Labor senator Doug Cameron has given notice of a motion which would give Senator O'Sullivan's bill precedence over all government business, with the expectation there will be a vote to approve it next week.
The Senate would also prioritise a bill to scrap the Fair Work Commission's four-yearly review of modern awards, ahead of parliament adjourning for the year on December 7.
Greens senator Peter Whish-Wilson, who has been working closely with Senator O'Sullivan, said the Senate was "close to having another big victory" following the passing of laws to allow same-sex marriage on Wednesday.
The O'Sullivan bill is now close to legislation the Greens had previously tried to introduce.
"We will now have a fair dinkum inquiry," Greens leader Richard Di Natale said in anticipation of the bill passing both chambers of parliament.
"My message to every banking CEO across the country - get ready for an inquiry, it's coming, it's coming fast and you are going to have to answer to those victims that you preyed on for so long."
Senator Whish-Wilson said it would be a very brave government that resisted the will of both houses by not providing any inquiry with funding.
Attorney-General George Brandis argues an inquiry is a waste of money and would take too long to deliver any relief to customers already benefiting from government reforms.
Cabinet colleague Josh Frydenberg insists the government is already focusing on getting a better deal for bank customers.
"That's why we've supported a greater transparency and accountability regime for executives, that's why we supported a complaints authority, that's why we've beefed up the resources of ASIC," he told reporters on the hustings in the Sydney seat of Bennelong.
But Nationals senator John Williams, who is supporting Senator O'Sullivan's push, thinks an inquiry is getting closer with the support of two of his colleagues in the lower house, George Christensen and Llew O'Brien.
