Helen Liddell, Economic Secretary to the Treasury, indicated the role might be assumed by the new all-powerful Securities and Investments Board when it takes over the Bank's supervisory responsibilities.
However, senior Treasury sources insisted the Bank would continue to play a "critical role" in overseeing the financial stability of the banking system.
Responding to weekend reports that the Bank would lose its status as lender of last resort, Mrs Liddell said: "The reason we are flagging up this issue so early is because we want to consult as widely as possible and bring people along with us. It is something we have to take the advice of the Bank and Treasury officials on."
She pointed out, however, that even now the Bank's ability to act as lender of last resort was limited and that it did not have the resources to bail out a big bank. Speaking en route to Paris for today's OECD meeting, she said: "If there was a major banking crash now involving a high street clearer, say, then the reality is the state would have to be involved."
Bank officials accept that in many instances the Treasury would be the de facto lender of last resort. The Bank performed this function after the collapse of Johnson Matthey Bankers in the 1980s and the National Mortgage Bank but it would not have been able to act as lender of last resort if it had been deemed necessary to rescue Barings which crashed with debts of pounds 800m.
What the Bank is more concerned about, however, is where lines of responsibility will lie when the SuperSIB is up and running, which body takes the lead role in deciding whether or not the collapse of a bank carries a systemic risk to the banking system and who decides whether it needs to be bailed out.
The answer appears to be that the beefed-up SIB, to be run by the present Deputy Governor of the Bank of England, Howard Davies, will be responsible for the prudential supervision of banks. But if the stability or liquidity of the banking system is threatened or there is a risk of "contagion" from one bank failing, it will be the responsibility of the Bank, in consultation with the Government and the SuperSIB.
While this is welcome news for the Bank after the way its regulatory functions were removed without consultation last week, some observers question how comfortably this would sit with the loss of its role as lender of last resort.
Both the Bank and the Treasury are still recovering from the handling of last week's announcement that the Bank was to lose its responsibility for banking supervision. The climate of uncertainty was not helped by suggestions from "senior Treasury ministers" that Mr George had "played into our hands" by confiding he thought about resigning over the move.
The remark, apparently designed to undermine Mr George and force him out, enraged a number of senior City figures, including the chairman of NatWest, Lord Alexander. Martin Taylor, chief executive of Barclays, is also thought to have been angered. However, relations between the Bank and Treasury were patched after Mr Brown's economic policy adviser, Ed Balls, met the Governor for lunch last Friday. The two are said to have emerged smiling and harmonious.