Sir David faces strongest competition for the governorship from Eddie George, deputy governor of the Bank, and from Sir David Walker, who is a Bank director, former chairman of the Savings and Investments Board and who was recently appointed deputy chairman of Lloyds Bank.
City speculation that Sir David Scholey's directorship at GEC meant that he knew he was out of the running for the Bank appointment is wide of the mark, insiders believe. He might simply have taken an opportunity that arose, and if offered the governorship, could resign his GEC job, they said.
The Prime Minister's office is expected to announce the identity of the new Governor by the end of January, although the appointment could be made before the new year.
Robin Leigh-Pemberton comes to the end of his second term as Governor on 30 June.
Insiders last week were discounting the chances of other names in the frame as also-rans. Sir Christopher Hogg, chairman of Courtaulds Textiles, is thought to be a long shot because he has no banking experience and only became a director of the Bank last year. Sir Peter Middleton, chairman of Midland Bank; Lord Alexander, chairman of National Westminster, and Sir Nicholas Goodison, chairman of TSB Group, are also well behind the front runners, partly because clearing banks are out of favour with the public and with many politicians.
The chances of Sarah Hogg, chief policy adviser to the Prime Minister, suffered following the debacle of Black Wednesday.
Sir Denis Weatherstone, the widely respected chairman of JP Morgan, the US bank, is also not thought to be a serious candidate. Although an Englishman, he recently adopted US citizenship, which would not help his chances. 'Why would he want the job?' one insider asked. 'He is one of the Great and the Good on Wall Street, not the City. He might want a job on the Federal Reserve Board, but surely not over here.'
Despite the heavy speculation, the appointment could go to a complete outsider - just as no one in the City had predicted Mr Leigh-Pemberton's appointment 10 years ago.
'It is a political appointment in the end,' said one observer. The decision is made by the Prime Minister in consultation with the Chancellor and is confirmed by the Queen.