Dr Lowe, who instigated an interest rate tightening cycle in May last year, is widely expected to leave when his time is up in September.
But senior Liberal Jane Hume said he should be reappointed.
"We're in the middle of a cost-of-living crisis right now," the senator told Nine's Today show on Thursday.
"Consistency is very much the key to managing the economy.
"He is certainly well qualified to stay in the position."
Senator Hume, who is chair of the Senate select committee on the cost of living, said Dr Lowe had been unfairly demonised by the Labor government for doing his job by lifting interest rates to bring down high inflation.
"Like the government have pointed to high rates and said 'see, that's his fault'," she said.
"Poor old Philip Lowe is doing his job."
Senator Hume said "his job is to keep the inflation in that band" of two to three per cent across the course of the economic cycle.
Inflation is currently running at about six per cent.
Speculation continues to mount about who the government could select to replace Dr Lowe.
Potential candidates so far include Treasury Secretary Stephen Kennedy, Finance Department Secretary Jenny Wilkinson, RBA Deputy Governor Michele Bullock and high-ranking former RBA officials David Gruen and Guy Debelle.
Treasurer Jim Chalmers is expected to announce the decision on whether to continue Dr Lowe's tenure or replace him by the end of this month.
Dr Lowe has weathered criticism about the central bank's hardline rate hiking cycle, which is hurting households with mortgages already battling the rising cost of living.
He's also been attacked for telling Australians in 2021 that there would be no rate hikes until "at least 2024".
The RBA has raised its cash rate 12 times since May 2022, with pauses in April and this month.
The cash rate currently sits at 4.1 per cent.
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