A new leader is expected to be installed at the Reserve Bank, marking the end of Philip Lowe's seven-year tenure in the top job.
Dr Lowe's term is due to end later in the year and federal treasurer Jim Chalmers has confirmed a decision will be made on the central bank's leadership this month.
Multiple media outlets reported on Friday that the governor would not continue in the top job, although the government remained tight-lipped on its decision.
Leaders would also not confirm if a decision would be made on Friday morning during a cabinet meeting, as was widely anticipated.
Deputy Prime Minister Richard Marles told Nine's Today program the government was still "going through our processes in relation to that position" when asked about the appointment.
Opposition Leader Peter Dutton does not want a senior bureaucrat in the role, with Treasury secretary Steven Kennedy and Finance secretary Jenny Wilkinson on the shortlist of likely candidates.
"You can't have somebody who is in the pocket of the treasurer or the finance minister," he said.
But Mr Marles said the Liberal leader was "playing politics" and any of the potential Reserve Bank governors would be independent.
"There are lots of people in government who work very closely with the government of the day," he said.
The Reserve Bank's deputy governor, Michele Bullock, is also considered as a leading contender.
Dr Lowe's term is due to expire in September.
The governor has faced criticism after embarking on an aggressive string of interest rate hikes after suggesting the cash rate would not move higher until 2024 .
© AAP 2023