In a sign that negotiations may be reaching their final stages, U.S. Attorney General Loretta Lynch last week met with Credit Suisse chief executive Tidjane Thiam, another person familiar with the matter said.
A potential resolution could come as early as this week.
The sources did not want to be identified because the negotiations are not public.
Credit Suisse and the Department of Justice declined to comment.
The penalty stems from a 2012 initiative launched by U.S. President Barack Obama to hold banks accountable for selling mortgage debt while misleading investors about the risks, a practice that helped cause the worst economic crisis since the 1930s.
The penalties, which for U.S. banks reached $46 billion, are set to deliver another setback to European lenders, many of which remain fragile, with scant capital, in the wake of the financial crash.
After record settlements were reached with U.S. banks such as Bank of America and JPMorgan, the focus has turned to Europe's Deutsche Bank, Royal Bank of Scotland, Credit Suisse, Barclays , UBS and HSBC.
News in September that the Justice Department made an initial demand of Deutsche of $14 billion to settle its case sent the German lender's stock plummeting and raised fears Credit Suisse could also face a stiffer penalty.
Just prior to Deutsche confirming that the Department of Justice was seeking $14 billion, JP Morgan analysts estimated Credit Suisse's fine at around $2 billion.
Deutsche Bank could this week agree its penalty over the sale of toxic mortgage debt, one person with direct knowledge of the matter said on Monday. The bank has said it expects to pay materially less than $14 billion.
Credit Suisse's litigation provisions at the end of 2015 totalled 1.605 billion Swiss francs ($1.56 billion). In November, the bank said it had upped litigation provisions by 357 million francs, mainly in connection with mortgage-related matters.
In addition to the Justice Department probe, Credit Suisse is defending itself against lawsuits by the New York and New Jersey attorneys general over similar claims involving billions of dollars of investor losses.
If Credit Suisse reaches a settlement with federal authorities, it will likely settle with the states as well.
A New York attorney general spokeswoman declined to comment, and New Jersey did not immediately return a call for comment.
President-elect Donald Trump takes office on Jan. 20, which means key government players involved in the negotiations would change, complicating the banks' efforts to reach settlements.