Policymakers have set the seven per cent threshold as the stage at which it will look at hiking rates.
But if they believe there is no risk of inflation rising too far, the Bank could push the unemployment threshold further down, he said.
The policy is designed to give households and firms more certainty on when interest rates will at last increase.
However, the deputy governor cautioned that this point may be some way off, arguing the economic recovery is still relatively slow.
“The need to restore the public finances to sustainability means that fiscal consolidation will continue for some years yet,” he told the Society of Business Economists.
“And, for some households, the past accumulation of debt may weigh on spending.”