Such an appointment would also put Mr Davies in pole position for the governorship when Eddie George's tenure ends next May. He is one of the most respected of City economists - as well as being an Independent columnist - and his wife, Sue Nye, is Gordon Brown's assistant.
The Chancellor's unexpected move, which gave effective independence to the Bank 51 years after it was nationalised by Clement Attlee's landslide Labour administration, marked a dramatic shift in the new Chancellor's attitude to an independent Bank that was greeted with unconditional approval by financial markets. Bond and equity traders now expect inflation and interest rates to stay low and the pound to weaken from its recent strength.
The move, which was dubbed the most far-reaching in the Bank's 300-year history, drew the final curtain on the "Ken and Eddie Show", as the monthly meetings between the former Chancellor Ken Clarke and the Bank's governor Eddie George were affectionately known, bringing to an end the increasingly personalised encounters that had characterised the setting of monetary policy.
The expected appointment of Gavyn Davies to the deputy governorship is part of the creation of a monetary policy committee which will comprise the governor, his two deputies and six other members. Four of the committee will be government appointments who are recognised experts in monetary policy.
Academia is well represented in the list of those being tipped for the remaining slots on the committee, with the odds shortening on David Currie, a London Business School professor and working Labour peer, Charles Goodhart, a former Bank of England adviser who is currently a professor at the London School of Economics, Richard Portes, from the London Business School, and John Flemming, another ex-Bank man from Nuffield College, Oxford.
Runners and riders from the City include Tim Congdon, a Treasury wise person and hard-line monetarist and Paul Mortimer-Lee, chief economist at Paribas.
It is thought an industrialist is likely to feature on the committee, with Sir David Simon of BP a possibility.
The committee will meet once a month to decide whether interest rates need to be changed, using a government-set inflation rate target (currently 2.5 per cent) as a benchmark. Any changes will be announced immediately, with the minutes of the meetings released within six weeks of the meeting.
The removal of interest rate decisions from the Chancellor marks a dramatic shift towards a fully independent central bank.
The new regime is understood to have been modelled on New Zealand's, where the central bank is also charged with meeting a government-set inflation rate target. In Europe, the French and German central banks are given a more genuinely independent remit of achieving "price stability", which they determine.
The proposed changes end the Chancellor's monthly meetings with the governor of the Bank. Norman Lamont established that formal ritual back in October 1992 in the wake of sterling's crash out of the ERM when a commitment arose to keep to a strict inflation target which the Bank would have a part in setting.
It was Mr Clarke's innovation in 1994, soon after his appointment, which saw minutes published six weeks after each meeting, bringing interest rate policy out into the open. The meetings were peppered with sharp disagreements between the Mr Clarke and the Governor.