His warning chimes with comments from Bank Governor Sir Mervyn King last week about the dangers of mixing monetary and fiscal policy.
The QE gilt purchases are funded by the issuance of central bank reserves and are aimed at boosting money supply and economic activity.
In a speech in Hull, Mr Bean said: "Should the Bank's holdings of gilts just be cancelled? The idea is that this would relieve the Government of having to levy the taxes to pay both the coupons on the gilts and the principal when it falls due [to be paid]. Government debt would fall at a stroke of the pen, apparently relieving the future burden on the taxpayer.
"Unfortunately this is not as good an idea as it sounds. Cancelling the gilts would deprive the Bank of the assets it needs to sell back to the market in order to suck the bank reserves out when the time comes to unwind the policy. It would also deprive the Bank of the wherewithal to pay the interest on the reserves in the meantime, so we would need either to keep Bank rate perpetually at zero or else be willing to continue issuing additional reserves indefinitely in order to meet our obligations."
He added: "One can easily see how this would eventually lead to inflation taking off."
Some commentators have said Financial Services Authority chairman Lord Turner, because he has talked about further policy innovations, might favour the Bank telling the Treasury it never has to repay some of the debt bought through the QE programme. He has been touted as a possible successor to Sir Mervyn.