Bank of America and the Justice Department are close to a deal in which the bank will pay between $16 billion and $17 billion to resolve allegations of mortgage-related misconduct in the run-up to the financial crisis, according to people familiar with the matter.

The bank has agreed to pay roughly $9 billion in cash to the Justice Department, states and other government entities, these people said, with additional money aimed at consumer relief, such as reducing mortgage balances for struggling homeowners.