It comes after official figures showed UK inflation eased back to its lowest level for more than two years last month, lowering the cost of servicing national debt.
With inflation coming down and hopes for interest rate reductions next year, economists have predicted that the Chancellor could see his headroom roughly double as a result.
This could allow him to cut personal taxes in the spring 2024 Budget, which he is expected to use to set the tone for a general election which could take place later in the spring or autumn.
But he cautioned that it is not clear what he can do before he sees the new Office for Budget Responsibility forecasts next year.
“If debt interest payments go down then potentially that gives me more headroom and I could use that in lots of different ways, but I would never use it in a way that would compromise the battle against inflation,” Mr Hunt said.
“We would like to bring down the tax burden in a way that is responsible.”
The Chancellor began to ease the historically high tax burden in his November autumn statement by cutting national insurance and announcing savings for businesses, delighting Tory MPs who have long lobbied for tax cuts.
Despite the earnings bonus, millions of workers will face a squeeze on their finances with the tax burden still set to reach a record high.
On Wednesday, the Office for National Statistics said the rate of Consumer Prices Index inflation fell to 3.9% in November, down from 4.6% in October, and the lowest level since September 2021.
Mr Hunt said there is “still work to do” in bringing down inflation and that it continues to be ministers’ immediate priority.
A faster rate of decline in inflation could also prompt the Bank of England to cut interest rates, something which would ease the financial pressure on mortgage holders in election year.
The Chancellor declined to comment on the outlook for interest rates, but said: “I think people will start feeling more optimistic about their personal finances if they see interest rates on a downward trajectory.”