National Australia Bank CEO Philip Chronican is concerned the Reserve Bank's monetary policy has lost its potency and there needs to be other ways of driving economic growth.
But his ANZ counterpart Shayne Elliott does not believe rates will turn negative.
The central bank's cash rate stands at just 0.75 per cent after three cuts this year.
Financial markets are predicting the central bank will make another cut in the rate early next year fuelled by the recent crop of weak data - slow retail spending, slowing wages growth, a drop in the number of people employed and a rise in the jobless rate to 5.3 per cent.
"My concern about the current very low levels of interest rates have largely exhausted our fire power on monetary policy," Mr Chronican told the House of Representatives economic committee in Canberra on Friday.
Speculation among economists is that once the cash rate is cut to 0.5 per cent, the central bank will start considering other forms of monetary policy, such as quantitative easing where it would buy securities to increase the money flowing through economy.
Adding to the speculation is RBA Governor Philip Lowe booking in to give a speech entitled "Unconventional Monetary Policy: Some Lessons from Overseas" at a business dinner in Sydney on November 26.
Mr Chronican believes such policy moves will just depress interest rates further.
Separately, the head of ANZ Bank Shayne Elliott told the committee that he saw the chance of interest rates turning negative as "incredible low" and is not even sure under his bank's terms and conditions it could actually offer them to depositors.
"Personally, I'm not predicting we'll end up with negative interest rates," Mr Elliott said.
Even so, the bank thinks it is prudent to test its systems for a negative interest rate environment, but Mr Elliott said it goes beyond the technology.
"I don't know whether it's permitted under our terms and conditions on deposits to even have negative interest rates," he said.
Mr Chronican is concerned that rates are now so low, the Reserve Bank has nothing to fall back on should the economy suffer a global shock.
"If we want to see growth in the economy, we need to look at other forms of growth-promoting activity," Mr Chronican said.
There is speculation the federal government could bring forward already legislated personal income tax cuts that are due to start in 2022, perhaps being announced as early as next month's mid-year budget review.
"We will always consider ways in which we can cut taxes to help people make decisions about their own spending," cabinet minister Peter Dutton told the Nine Network on Friday.
However, Finance Minister Mathias Cormann talked down the prospect of packing more measures to stimulate the economy into the half-yearly budget update.
"We delivered a pro-growth budget on April 2 and it is a plan that we took to the last election to build a stronger, more resilient economy where more jobs are being created," Senator Cormann told Sky News.
"That is the plan that we are implementing, that we are delivering on, that's what we promised to the Australian people that we would do, and that is what the Australian people expect us to do."
Australian Associated Press