Mark Carney told MPs the majority of the rate-setting monetary policy committee felt a rise may be need to ensure “sustainability”.
He was being quizzed by the Treasury Select Committee hours after new figures showed rising food and transport costs had pushed the headline measure of inflation to three per cent in September.
Inflation is at its highest since April 2012 and the trend raises the prospect of the Bank of England increasing interest rates next month.
The Bank is tasked with keeping inflation around two per cent with the governor having to write to Chancellor Philip Hammond with an explanation if it edges above three per cent.
Mr Carney told MPs that “having seen some early evidence of building domestic pressures, the judgment of the majority of the committee is that some raise in interest rate in coming months may be appropriate in order to have that sustainability.”
The rise in inflation points to the growing pressure on household finances which would intensify with an increase in interest rates triggering higher mortgage costs.
A Treasury spokesman said: “We understand that families are feeling the effects of inflation and we are helping them with their living costs.
“We’ve frozen fuel duty, doubled free childcare for nearly 400,000 working parents and cut income tax for 30 million people. Increases to the national living wage are also delivering the fastest pay rise for the lowest paid in 20 years.”
The inflation figures led to fresh calls for the chancellor to end the freeze on public sector wages and benefit rises in his Budget next month.
September’s inflation figure is usually used to calculate benefit rises for the following year but the Government has imposed a freeze on working-age benefits.
David Finch, senior economic analyst at the Resolution Foundation said: “Rising inflation is dealing a double living standards blow to families on low and middle incomes, who are facing shrinking pay packets and reduced state support.
“But rather than addressing the squeeze, government policy is making things worse by freezing benefits at a time when inflation is almost three per cent.
“The chancellor should use his Budget next month to unfreeze working age benefits and provide some much-needed relief for young families in particular.
“He could fund the policy by freezing the personal tax allowance which would bring in around £2bn, largely from better from households.”
The so-called pensions triple-lock means they will rise by three per cent in April.
The Retail Price Index, which is used to set next year’s business rates, was unchanged last month at 3.9 per cent. Business groups have argued the rates rise should be put on hold given the level of economic uncertainty.