The governance structure would be at odds with an independent review into the bank that recommended an external chair be appointed to helm the second board tasked with running the institution's finances and organisational strategy.
The federal treasurer confirmed this was one of the finer details from the review the central bank and the government were still nutting out.
Jim Chalmers said the review itself made it clear that it was a "line-ball call" as to whether the governor should chair both boards or not.
Other items under active discussion included term limits, as well as the possibility of including the deputy governor and the chief operating officer on the governance board.
"And so I've been consulting on all of that, and then there are a small handful of issues," the treasurer told journalists on Friday.
Former RBA governor Ian MacFarlane raised a number of issues with the new board structure earlier in the week, including that the new dual-board model would give part-time board members the majority of the votes in monetary policy decisions.
Dr Chalmers said it was an unusual critique given the majority of people sitting on the monetary policy setting board were already external members.
A three-person review panel recommended a suite of reforms to boost the central bank's leadership and decision-making earlier this year.
Central to the panel's recommendations was the creation of two separate boards, one responsible for governance and the other for monetary policy, which sets interest rates.
The review also called for governor-led press conferences after monetary policy meetings, with board members occasionally speaking publicly on the decisions taken.
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