Mizuho was hit by the glitch last month after accounts were flooded with donations for a magnitude 9.0 earthquake and tsunami in northeast Japan that killed up to 28,000 people.
The computer troubles forced shutdowns of Mizuho's automatic teller machines and disrupted transactions, adding to the woes of businesses and households already badly shaken by the disasters.
Mizuho Bank's president, Satoru Nishibori, is seen compiling a plan to prevent a recurrence of such glitches and formally announce his resignation by a shareholders' meeting in June, the Asahi said, without citing a source.
Candidates to replace him include Manabu Yoshidome, Mizuho Bank's deputy president, and Takashi Nonaka, president of Mizuho Trust & Banking, the Asahi added.
Some form of punishment for Mizuho Financial Group President and CEO Takashi Tsukamoto is also being considered, the newspaper said.
(Reporting by Chisa Fujioka; Editing by Robert Birsel)