Sterling rose to $1.2936 against the dollar after Mark Carney said that "some removal of monetary stimulus is likely to become necessary", BBC reported.
He said a change would depend on whether company investment could offset a slowdown in consumer spending.
Mr Carney said it was an issue the Bank "will debate in the coming months".
Pound Sterling - United States Dollar
Last week, at the delayed Mansion House gathering in London, Mr Carney said that "now is not yet the time to begin" raising interest rates which remain at a record low of 0.25%.
However, shortly afterwards, Bank of England chief economist Andy Haldane said he might vote for a rate rise before the end of the year.