A Wells Fargo spokeswoman declined to comment. Representatives for the Justice Department and the S.E.C. did not immediately respond to requests for comment.

The settlements would be the latest in a series of government penalties against the bank and its former leaders. Just last month, former Wells Fargo executives who presided over the abusive sales practices — including a former chief executive, John G. Stumpf — were subjected to the largest fines ever assessed by bank regulators.

The scandal erupted in 2016 when Wells Fargo revealed that it had opened millions of bank accounts in customers’ names without their knowledge while charging other customers unnecessary fees for auto and home loans. It also admitted to selling some customers unwanted insurance products.

While the settlements would resolve yearslong investigations by the agencies, they would not end the bank’s regulatory woes. For two years, the bank has been operating under growth restrictions imposed by the Federal Reserve, which has said it will not release the bank from those constraints until its leaders can demonstrate that they have restructured its operations to prevent similar abuses.

Regulators are also still seeking penalties against former employees.

On Jan. 23, the Office of the Comptroller of the Currency fined former top executives millions of dollars each; Mr. Stumpf agreed to pay $17.5 million. But others, including Carrie L. Tolstedt, Wells Fargo’s former head of retail banking, are fighting the cases brought by the regulator, which is seeking a $25 million fine against her.