Should the BoE set negative interest rates it would mean the central bank would be able to charge banks interest for holding onto their money.
The move had previously been ruled out due to the potentially crippling damage it would do Britain’s building societies which are more dependent on deposit income than banks.
The Daily Telegraph reported that Tucker told the Treasury Select Committee: “This would be an extraordinary thing to do and it needs to be thought through carefully.
“I hope that we will think about the constraints of setting negative interest rates."
Tucker also suggested extending the Funding for Lending scheme to non-bank lenders.
However Tucker stressed “nobody on the [rate-setting] committee thinks that quantitative easing has reached the end of the road.”