The split of the two roles was promised five months ago.
Reading from a prepared statement, Mr Buxton said: 'I am pleased to say that we are at an advanced stage. It is my intention to make an appointment as soon as possible, but it is always difficult to forecast how long a search will take for an important executive position.'
Investor demands for the roles to be split bubbled to the surface last summer and mounted in the autumn as the bank's fortunes were falling fast.
In January Mr Buxton said the board would revamp Barclays' management structure. He formally announced the search in March. The delay in finding a number two has also sparked speculation that Mr Buxton is reluctant to relinquish power.
'I originally thought it would take about four months,' he said yesterday. But he added that five months was not a long time compared with how long other companies took to choose their top executives.
'We have had some very high quality candidates, so there is no truth to the rumour that we are having difficulties finding candidates.'
Mr Buxton, formerly group managing director, was chosen in spring 1992 to succeed Sir John Quinton as chairman in January 1993, taking on both chairman and chief executive roles.