The Financial Services Agency has urged Sumitomo Mitsui Trust Bank and Mizuho Trust to take preventive steps, the Nikkei said, without citing sources.
The two banks said this month they found vote-counting problems at 1,346 companies that entrusted them with counting shareholder mail-in votes for annual general meetings.
Sumitomo and Mizuho declined to comment.
The banks attributed the miscounts to procedures during the peak season for such meetings, saying they usually ask the post office for delivery a day earlier to ensure more time to count the forms.
But they do not issue receipts until the day after delivery, meaning that some forms were mistakenly categorised as having passed the deadline despite delivery on time, according to the banks.
(Reporting by Takashi Umekawa; Editing by Tom Hogue and Clarence Fernandez)