As speculation mounts on whether Philip Lowe will be replaced as head of the RBA once his term expires, Mr Dutton said the potential successor should not come from the public service.
Two of the leading candidates for the position are Treasury secretary Steven Kennedy and Finance secretary Jenny Wilkinson.
But Mr Dutton said the next governor should be someone from a non-political background given the importance of the position.
"We don't believe it should be somebody who is familiar, if you like, to the government, somebody who has been working very closely with the treasurer or the finance minister or the prime minister," he told Sydney radio station 2GB on Thursday.
"We don't want somebody there who's been involved in the political process at a senior level."
Dr Lowe's term as Reserve Bank governor is due to expire in September.
Deputy governor Michele Bullock is also seen as a leading contender.
Treasurer Jim Chalmers has said a call on whether the term would be extended or a new governor be appointed would be made shortly, and has held talks with shadow treasurer Angus Taylor about the decision.
Dr Lowe has faced criticism following multiple interest rate hikes in the past year, after previous comments saying the cash rate would not increase until 2024.
Cabinet minister Chris Bowen rejected suggestions the next RBA chief should not be from the public service.
"That's an insult to departmental people," he said.
"Mr Dutton should respect that whoever is RBA governor at any given time will be governing themselves with all rigour and independence that other governors have.
"I think Mr Dutton should reflect on his comments."
The opposition leader said bipartisan support for the appointment was critical.
"The Reserve Bank is one of the country's most important institutions, like the High Court - we don't want political appointments," Mr Dutton said.
He said the governor needed to have independence because they made tough calls on interest rates "in our country's interest, even if they're unpopular calls".
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