The board will also be briefed on options if the bank's chief executive Kenneth Lewis is charged with civil fraud, according to the paper.
Last week, New York Attorney General Andrew Cuomo subpoenaed five current or former Bank of America directors to learn what they knew about Merrill Lynch & Co's problems as the companies prepared to merge.
Cuomo has threatened to sue Bank of America officers, perhaps including Chief Executive Kenneth Lewis, and its lawyers over a lack of disclosures about the merger, which shareholders approved last December 5 and which closed on January 1.
The bank's directors were not surprised by any of the allegations made by Cuomo's office and back Lewis, the Journal said, citing the person familiar with the matter.
Bank of America and DuPont could not be immediately reached for comment by Reuters outside regular U.S. business hours.
(Reporting by Ajay Kamalakaran in Bangalore; Editing by Muralikumar Anantharaman)