The Journal said that the investigation is in its early stages and that prosecutors have yet to decide whether they would pursue a civil or criminal case, should they choose to. The bank has been issued a supboena, people familiar with the matter told the Journal.
Later on Wednesday, Reuters also reported that federal prosecutors are investigating the bank regarding its sales practices.
Shares of Wells Fargo closed down 0.94 percent on Wednesday.
Wells Fargo declined to comment to CNBC.
Officials announced last week that Wells Fargo will pay $185 million in penalties and $5 million to customers for opening fee-generating accounts without authorization. Over a five-year period, 5,300 Wells Fargo employees were fired over the practice cited by the Consumer Financial Protection Bureau, CNBC confirmed. The activity occurred in the company's community banking division.
"I think the best thing I could do right now is lead this company, and lead this company forward," he told Jim Cramer in an interview on "Mad Money." Stumpf said that the company is sorry and deeply regrets "any situation where a customer got a product they did not request."
— CNBC's Abigail Stevenson contributed to this report.