Mr Quinn, whose responsibilities include banking supervision, has survived three major bank failures; the collapse of Johnson Matthey Bankers in 1984, that of BCCI in 1991 and Barings earlier this year.
Sources suggest that the 58-year-old has decided it is time to leave the bank when his contract expires early next year, when he will be 59.
In spite of criticisms of the Bank for regulatory failures in the Board of Banking Supervision's report into the Barings affair, the Bank has so far suffered only one casualty.
Christopher Thompson, a manager in the banking supervision department, resigned in July after being criticised by name for offering Barings an informal waiver allowing its exposure to its Singapore sub- sidiary to exceed 25 per cent.
Mr Quinn was not criticised in the report, and he was not in charge of supervision on a day-to-day basis. But the report concluded with a number of lessons for the Bank of England. These included a need to increase its understanding of the risks in the securities business and a plea for it to collaborate more closely with other regulators, in the UK and overseas.
Mr Quinn's departure is likely to be be presented by the Bank as his own decision after a long stint in the hot seat.
The normal retirement age for Bank of England employees is 60, but there is no firm rule for directors. They rarely remain past the age of 70, but quite often stay on into their sixties.
Yesterday the Bank would make no comment on whether Mr Quinn was likely to take on a third four-year term.
Treasury sources have suggested that ministers would have liked to see other heads roll at the Bank of England.
Sources close to the Bank say morale in the supervision department has been declining since the Bank was reorganised into separate monetary stability and financial stability divisions just over a year ago.
The Bank's high-flyers have opted to move into the monetary policy area. ''There is a real feeling that we are in a backwater. There is a lot of dissatisfaction,'' said one supervisory official.
This low morale is matched by the low opinion of supervisors held by some City bankers. According to a director of one leading investment bank, the officials are not of high enough calibre for the Bank of England to make a good job of supervision.
Eddie George, the Governor of the Bank of England, hinted as much when he told the Treasury and Civil Service Select Committee, at hearings on the Barings collapse, that it was difficult to attract and retain good supervisors.
At the time of Mr Thompson's resignation from the Bank, Alistair Darling, Labour's spokesman on City affairs, said he had been made a scapegoat for widespread supervisory weakness.
Yesterday the Bank of England hit back at suggestions by Nick Leeson, the former Barings trader, that it had mishandled the unwinding of the futures positions that caused Barings' downfall. Mr Leeson said that when he fled the losses at Barings stood at pounds 325m, but a week later they had grown to around pounds 830m.
The Bank disputed the figures and said that when it inherited the situation Mr Leeson's losses were already around pounds 600m. The total loss when the positions were closed by the administrators was around pounds 900m.
"The difference simply reflected the scale of the open positions and the adverse market movements," the Bank said yesterday. "The Bank had nothing to do with publicising the problems which were already becoming evident in Singapore at the end of the previous week.
But Mr Leeson accused the Bank of letting the situation get worse. "I mean they told everybody effectively through their actions," he said. "They told every market participant, there is going to be a big sell order on Monday. They're certainly guilty of the market being down a thousand or twelve hundred points on the Monday."
Apart from this, the Bank appeared to be relieved by the general thrust of the interview broadcast last night with Sir David Frost.
"Our report in July said that there was a rogue trader, that he seemed to have deceived his superiors by running this account, but that he did not appear to have stolen for himself. By and large Nick Leeson's account concurs with this," a source close to the Bank said.
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