Shirakawa has been deputy governor.
Party Secretary-General Yukio Hatoyama indicated the party would also back former Vice Finance Minister for International Affairs Hiroshi Watanabe as a replacement for Shirakawa as deputy governor, Kyodo news reported.
''We, the DPJ, approved deputy governor Shirakawa so I think it would be difficult from a logical point of view for us not to approve him as governor,'' Hatoyama said at a news conference.
The government is expected to make the proposals official Monday, the report said.
The bank has been without a governor since Toshihiko Fukui resigned from his five-year term on March 19.