Insider sources told the Financial Times that Mr Geoghegan is looking to replace outgoing chairman Stephen Green and reacted with anger to the suggestion the job may go to someone else.
"He was told the board was not ready to give him the chairmanship and he was not happy," one source said.
The final decision on who will be HSBC's new chairman is to be made at a board meeting next week, with former Goldman Sachs banker John Thornton among the favourites to get the job.
Others in the running are believed to include finance director Douglas Flint and non-executive director and current Rolls-Royce chairman Simon Robertson.
Earlier this month, Stuart Gulliver, investment banking head for HSBC, warned that the financial institution may move its headquarters out of Britain if the government decides to split up retail and investment banking divisions of large firms.
By Tony Aynsley