A review of Australia's central bank last year called for the mechanism to be ditched to bolster the RBA's independence.
But resistance is building to the government's plan to scrap the never-used power spelled out in section 11 of the RBA Act.
A range of high-profile figures said the mechanism should be kept during a hearing on Thursday, including former RBA governors Ian MacFarlane and Bernie Fraser and retiring Future Fund chairman and former coalition treasurer Peter Costello.
The Greens have been advocating for the power to stay in place, with economic justice spokesman Nick McKim vowing to move an amendment in parliament to keep it.
"As the Reserve Bank was smashing renters and mortgage holders with interest rate rises, (Treasurer) Jim Chalmers was working on a scheme to remove his own power to intervene," Senator McKim said on Thursday.
Michele Bullock, current governor of the central bank, used her appearance at the parliamentary hearing to confirm she was "agnostic" on the change.
Professor Renee Fry-McKibbin said removing the power would strengthen the RBA's independence (Mick Tsikas/AAP PHOTOS)
"I'm comfortable which ever way the government decides on this," she told the hearing on Thursday.
Two of the three reviewers appeared before the committee and outlined the case for scrapping the power.
Renee Fry-McKibbin, an economics professor at the the Australian National University, said the power had never been used, ditching it would strengthen the RBA's independence, and such a mechanism was not common internationally.
Also, under the changes, the parliament would still be able to step in if things were going awry rather than the government of the day.
Mr Macfarlane, governor of the RBA between 1996 and 2006, said scrapping the power would be a "big mistake".
If there was an "irreconcilable difference" between the RBA and the government - which he imagines would happen once or twice in a century - he said the power would be useful.
"It does play a useful role in the long-term relationship between the Reserve Bank and the government," he told the hearing.
Mr Costello said it was a "very difficult power to execute" that it could only be done in "very extreme circumstances", and he was ultimately happy with the restrictions in place at the moment.
"I can't see that you're going to improve things by getting rid of section 11," he said.
