Geoghegan, who was is understood to have been in line to receive a £4m payout, will donate his bonus to charity after the bank’s strong 2009 performance.
HSBC’s annual profits are likely to be between $11bn (£7.2bn) and $15bn (9.8bn).
The move follows a blockage of Geoghegan’s pay by shareholders after the bank intended to hand him a 36 per cent pay rise, bringing his salary to £1.4m.
Geoghegan and his wife are known for their support of educational charities, including Education Africa and Young Enterprise.
In a separate move, it is understood that Standard Chartered boss Peter Sands will make a payment to charity of a bonus expected to be around £1m when the bank reports record profits towards the end of the month.
Last week, Royal Bank of Scotland (RBS) boss Stephen Hester and Lloyds Banking Group chief executive Eric Daniels both waived their respective £1.6m and £2.3m bonuses after mounting pressure from shareholders and the public.
Barclays chief executive John Varley and president Bob Diamond declined to accept their bonuses last month even though their bank did not need a government bailout, setting a precedent for others to follow.