At least three key City figures have been approached and turned the job down, and it is understood that an appointment is still some way off.
Nick Verey of SG Warburg, John Thornton of Goldman Sachs, and John Nelson of Lazards have all been approached by headhunters working for Kleinwort.
A spokesman for Mr Verey, managing director of investment banking at Warburgs, confirmed that he had been contacted by the headhunters but 'had sent them packing. He is Warburgs through and through'. Mr Verey is a candidate for the top job at Warburgs and does not want to be seen as interested in moving.
John Nelson, managing director of corporate finance at Lazards, said: 'I don't comment on rumours like that.'
Mr Nelson worked at Kleinwort for 17 years before joining Lazards in 1986, and still regards it as his 'old school'. Lazards often works closely with Kleinwort. However, it is understood Mr Nelson is not interested in the job.
John Thornton of Goldman Sachs, one of the best-known deal- makers in the City, said he had not been approached by Kleinwort, but had been contacted by headhunters 10 days ago. He did not take it further.
He did, however, suggest that Kleinwort's specification for a new chief executive was similar to that which Barclays Bank drew up in its own search for a chief executive to join the chairman Andrew Buxton.
Mr Thornton suggested that the Kleinwort shortlist was similar to the Barclays list that produced Martin Taylor, the former Courtaulds chief executive. This would include people outside the City who have run big businesses but would not be out of their depth in financial services.
Kleinwort's main requirement is a good man-manager who can heal the rift between the corporate finance people and the stockbrokers.
Mr Agnew was victim of sweeping changes introduced by Lord Rockley when the latter replaced David Peake as chairman in May. Mr Agnew had been chief executive of Kleinwort for five years, supervising the integration of the stockbroker Grieveson Grant.
Critics inside and outside Kleinwort said that the securities side was not contributing enough to profits, and it was this split that finally led to Mr Agnew's departure, and the need for a new face from outside the firm to bring the two sides together.
It is thought that there are five or six names on the current shortlist. Headhunters have approached many more than that. They do not necessarily have to inform their clients whom they are contacting.
Some observers in the City are suggesting that Kleinwort should give up the search and let Simon Robertson, deputy chairman, get on with the job. Mr Robertson worked closely with Lord Rockley in the corporate finance department and wields considerable influence in the firm.
Both are keen to rebuild Kleinwort's client base, which they feel has been neglected over the past few years.
Tim Barker, deputy chief executive, is also close to Lord Rockley. Any outsider will have to be an impressive figure to take charge and reverse Kleinwort's relative decline.
Kleinwort, along with Cazenove and Barings, is one of the most blue-blooded institutions in the City. It was also one of the biggest players in UK merchant banking in the late 1980s, but since then has suffered a gradual decline relative to its competitors, exacerbated by internal feuding. The worst blow came in 1990 when the group made a pounds 34m loss after it failed to place a 29.9 per cent stake in the oil group Premier Consolidated.
Kleinwort has shown some signs of recovery, including a better- than-expected result for the half year to June, with profits doubled to pounds 42.2m. Mr Robertson is confident that the client list can be revived quickly, but much depends on getting the right chief executive.
Nobody from Kleinwort was available for comment yesterday.
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