Bank of America Corp. and the Justice Department are closing in on a landmark deal in which the bank will pay $16 billion to $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 federal government, states and other government entities, these people said, as part of an overall pact that could be finalized this month. Additional money would be aimed at consumer relief,...