On Friday, governor Mark Carney suggested they could rise from their current record low of 0.5 to around 2.5 per cent by early 2017.
Now Sir Charlie Bean has it would be "reasonable" to expect borrowing costs to return to pre-recession levels in the long term, between five to 10 years.
Homeowners have enjoyed a historically low 0.5 per cent base rate for five years but the level has caused misery for savers. Sir Charlie said: "It might be reasonable to think that in that long term you would go back to 5 per cent, but it's probably quite a long way down the road."
Mr Carney urges people to focus on the "big picture" rather than obsessing about when interest rates will rise.
It followed accusations that he had been behaving like an "unreliable boyfriend" by hinting at a rise this year, before appearing to back-pedal.
On Friday, Mr Carney insisted the important aspect for homeowners and businesses was that rates were likely to stabilise at around 2.5 per cent in three years' time, rather than the historically "normal" level of 5 per cent.
Sir Charlie said market expectations the first increase in interest rates would come at the turn of the year were "reasonable".
He added: "The market has rates going up to 2.5 per cent over next three years. That seems like a broadly sensible judgment."
Sir Charlie admitted that in the run-up to the crash, economists were "not sufficiently cognisant of the risks building up in the financial system".