The firm branded the speculation “offensive”, saying Geoghegan, who has been at the bank 37 years, has no intention of stepping down.
A spokesman said: “It is nonsense that Mike threatened to resign unless he was appointed chairman.
“The suggestion is offensive to both him and the company. As previously stated, the board is working under due process to finalise HSBC’s succession plan following Stephen Green’s already-announced departure and this proceeds in line with the scheduled timetable.”
Outgoing chairman Stephen Green will quit the firm in January to take up a full-time government role as trade and investment minister.