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.
The ABC reported on Friday that the governor will not continue in the top job.
The government has refused to comment on the fresh round of speculation and would not confirm if a decision would be made on the leadership on Friday, as widely anticipated.
Deputy Prime Minister Richard Marles was tight-lipped on the decision, telling Nine's Today program the government was still "going through our processes in relation to that position".
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 .
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