Varley was previously tipped as a frontrunner in the race to succeed Mervyn King as Governor when he retires next June, completing his second term in the post.
Treasury officials are drafting up a shortlist of candidates and will begin making formal approaches this autumn, with the ultimate decision on who will replace King in the hands of the Chancellor George Osborne and the Prime Minister.
The bookies have placed the banker – who was in charge of Barclays for almost seven years after becoming chief executive in September 2004 – as third favourite to take the top job at the UK’s central bank.
However, a source close to the situation said Varley has indicated he is not interested in the Governor job.
A spokesperson for Varley – who left Barclays last year and was replaced by Bob Diamond – was unable to confirm whether he has formally declined the position.
The Treasury said the official process of appointing a replacement Governor has not yet begun, but will be set out “in due course”.
Varley has a long-standing connection with Barclays, after he married Carolyn Thorn Pease, daughter of Sir Richard Thorn Pease, in 1981, becoming part of the Quaker Pease family. The Quaker Pease bank became part of Barclays in 1902.
Paddy Power is offering odds of 7/2 that Varley will take the hot seat, behind favourite Paul Tucker, King’s current deputy at the Bank, at 3/1. In the past, Chancellors have tended to appoint deputy governors to the top job – both King and Eddie George were deputies before they were appointed – and Tucker is seen as a ‘safe’ choice for the City.
Other names in the frame include Lord O’Donnell and Goldman Sachs Asset Management’s Jim O’Neill, at 4/1 and 5/1 respectively. Lord Adair Turner, the former head of the CBI and chairman of the Financial Services Authority, is also at 4/1 to head the Bank, while John Vickers, the former chairman of the Independent Commission on Banking, is at 16/1.
For those willing to take a more risky punt, the bookie is offering odds of 300/1 on former RBS boss Fred ‘the Shred’ Goodwin, while Spurs manager Harry Redknapp is at 1000/1.