The paper said Shinsei, owned 32.6 percent by buyout firm JC Flowers and Co., and Aozora, owned 53.6 percent by Cerberus Capital Management, had likely received approval from their major shareholders for the merger.
Jiji news agency had reported last month that the two shareholders were opposed to the merger.
Financial sources had previously said the banks aimed to reach a deal and announce the framework of the merger by May 13 when Shinsei is scheduled to report its earnings results for the last financial year.
The banks plan to set up a holding firm in 2010 and merge in a year or so afterward, the paper said. It added JC Flowers and Cerberus will likely remain shareholders in the holding firm.
Shinsei spokesman Eiji Otaka and Aozora spokesman Tsutomu Jimbo declined to comment on the report.
Both lenders were nationalised during Japan's banking crisis in the 1990s and later sold to foreign funds.
A new, merged bank would be on a stronger footing but will liekly need even more government money and may still struggle to compete in domestic lending against mega-banks such as Mitsubishi UFJ Financial Group, analysts have said.
Shinsei rose 8.2 percent to 145 yen and Aozora climbed 12 percent to 145 yen.