The final list of candidates is believed to include Reuters' head of global communications, Sholto Douglas-Home, the Inland Revenue head of marketing, Ian Schoolar, Shell's vice-president for global brands and communications, Raoul Pinnell, and the ISBA director of media affairs, Bob Wootton.
The news follows last week's decision by the COI deputy chief executive, Peter Buchanan, to rule himself out of contention for personal reasons.
He has been the acting chief executive since Fisher's departure in July.
The Government has recently bolstered its attempts to recruit a marketing heavyweight to replace Fisher by upping the salary of the position by £15,000 to £120,000 per year as well as offering the successful candidate a pension. The move was meant to prevent advertisers being deterred by the pay gap that exists between the public and private sectors.
A decision is expected to be made by the end of the year by a selection panel chaired by the Civil Service Commissioner, James Boyle. The panel includes Mike Granatt, the head of the Government Information and Communications Service, Peter Wardle, the Cabinet Office director, and the UKTV chief executive, Dick Emery. The successful candidate will work with the Prime Minister's strategy director, Alastair Campbell.
Schoolar said: "I am committed to my work on the revenue's long-term business direction and I intend to see this through - challenging though the COI position undoubtedly is."
Both COI and Douglas-Home refused to comment, while Pinnell and Wootton were unavailable as Campaign went to press.