The private equity firms may partner with First Republic Chairman James Herbert, the report said, citing one of the people.
Bank of America inherited San Francisco-based First Republic when it acquired Merrill Lynch & Co on January 1. Merrill had paid $1.8 billion for First Republic in 2007.
Carlyle, Blackstone and Bank of America were not immediately available for comment.
Bank of America has taken $45 billion of federal bailout money, and this week won approval of a capital-raising plan after regulators ordered the largest U.S. bank to raise $33.9 billion following a government stress test.
The Charlotte, North Carolina-based bank is also trying to sell its Columbia asset management unit.
Blackstone and Carlyle were part of a group that agreed to buy BankUnited Financial Corp
(Writing by Jonathan Stempel; Editing by Gary Hill)