Both men are due for retirement - Sir Brian is 65 in December and Sir Robin is already 70 - but Sir Brian is expected to be persuaded to stay on as chairman. Several candidates are being lined up to fill Sir Brian's shoes, with his two deputies leading the race.
Peter Ellwood, former head of the TSB, is regarded as hard-working and an ideal candidate to take over the role, as is fellow deputy Alan Moore.
Few outside candidates are being considered for the top position at the banking group which was formed last year out of the merger between Lloyds Bank and TSB.
Sir Brian, who became chief executive of Lloyds Bank in 1983, is seen as the driving force been the bank. Some banking analysts said, however, that while his chairmanship would ensure continuity in the management and strategy of the bank, it could hinder any attempt by the new chief executive to exert authority.
If Sir Brian becomes chairman, he will have to work closely with the new chief executive to oversee the ongoing integration of Lloyds and TSB.
The bank's intentions for life insurance, in which it is represented by TSB Life and Lloyds Abbey Life, puzzles analysts. However, there has been speculation in the stock market recently that Lloyds will buy up the remaining 37 per cent stake in Lloyds Abbey Life to bolster its TSB Life operation.
The bank is expected to keep its mortgage lending arm, Cheltenham & Gloucester, the building society it bought last year, as a separate entity.Reuse content