An insider told Bloomberg that the bank is due to announce the move when it releases its full-year earnings report on May 14th 2010.
Mizuho is set to make the sale in an attempt to bolster its capital levels, ahead of planned new global legislation requiring banks to hold more credit.
The firm is in a vulnerable position after losing around $8 billion on investments in the US mortgage market due to the financial crisis.
Kristine Li, a credit analyst based in Singapore for Royal Bank of Scotland, said even a share sale on this scale may not be enough for Mizuho.
"It will be tough for Mizuho to convince the market that this deal will be enough to meet new global capital regulations," she said. "Mizuho's core capital position is the weakest among major Asian banks."
Last month, Mizuho Securities USA, one of the subsidiaries of the Mizuho Financial Group, appointed James Wilders Reed as its new chairman - making him the first person from outside Japan to hold such a senior position within the firm.
By Asim Shah