After CEO Tim Sloan's abrupt departure from Wells Fargo (WFC -1.10%) last month, the company announced that it would search for a replacement externally, to the delight of many investors and regulators.

However, Warren Buffett, the CEO of Berkshire Hathaway (BRK.A -0.18%) (BRK.B 0.04%), doesn't think that focusing on external candidates will be enough. He believes that candidates with a certain type of financial industry background would do little to change regulators' opinions of the bank's cultural issues.

Warren Buffett smiling and greeting investors.

Warren Buffett has some advice for Wells Fargo. Image source: The Motley Fool.

What Buffett thinks Wells Fargo should do

When a big bank or Wall Street firm is looking for a new CEO, it typically does one of two things. It either hires one of the company's existing executives -- like Goldman Sachs (GS -1.18%) recently did with David Solomon -- or it hires an executive from a competitor.

In Wells Fargo's case, the first option is out. The bank has already said that it's only going to pursue external candidates. But Buffett doesn't think the second standard option would be a smart way to go, either, especially if the competitor is one of the Wall Street investment banks.

In an interview this week with The Financial Times, Buffett said that regulators and key players in Congress wouldn't be happy if Wells Fargo hired another Wall Street executive. "They probably shouldn't come from JPMorgan (JPM -1.26%) or Goldman Sachs," he said.

To be clear, Buffett isn't advising Wells Fargo to avoid all banking executives. After all, Wells Fargo shareholders (of which Buffett and Berkshire Hathaway are the largest, with a nearly 10% stake) should want the next CEO to have a great deal of banking experience. For example, a former CEO of a large bank that isn't Wall Street-based could still be a good idea.

Wells Fargo's biggest issue, and how Buffett's advice would help

At this stage of the recovery from the scandals of the past few years, Wells Fargo's top priority should be to convince regulators that it has made enough changes to ensure the past won't repeat itself.

Wells Fargo has clearly made some pretty big cultural changes, including getting rid of sales-based incentives for branch employees. In the minds of many regulators, however, the biggest lingering problem was that some of the executives that were in charge during the scandals were still there. And not only that, but the president and COO at the time, Tim Sloan, had been "rewarded" with the CEO job back in 2016 after the former leader stepped down in the wake of the fake-accounts scandal.

Now that Sloan is gone, a new CEO could be just what Wells Fargo needs to move on, especially in the all-important eyes of regulators. For example, Sen. Elizabeth Warren, a Massachusetts Democrat, personally requested that the Federal Reserve continue to restrict Wells Fargo's growth until Sloan was gone. And bank employees recently told Fed officials that Sloan's efforts hadn't transformed the bank's culture nearly as much as he had claimed.

However, a new external CEO might not be enough to satisfy everyone, especially if it's another Wall Street veteran, whom many in power (like Warren) see as part of the problem, not part of the solution. Wells Fargo can't truly move on until it's allowed to grow, and it needs the Federal Reserve's permission to start trying to grow again. Buffett may be right: A banking veteran who doesn't come from Wall Street could be the right person for the job.

The big question

Will Wells Fargo listen to Buffett? That's the billion-dollar question. While Wells Fargo hasn't publicly named any CEO candidates yet, the rumored short list includes former Goldman Sachs executives Gary Cohn and Harvey Schwartz (both deny interest in the job), as well as JPMorgan Chase CFO Marianne Lake. In a nutshell, Buffett is hoping Wells Fargo doesn't hire any of the three.

There are also some names from outside Wall Street who have been rumored as candidates, such as former U.S. Bancorp (NYSE: USB) head Richard Davis. Wells Fargo has refused to comment on any of the rumors.

Buffett continues to believe in Wells Fargo's business, saying that the scandals really haven't cost the bank a significant number of customers. However, being unable to grow in what's arguably the best growth environment for banks in decades isn't exactly what an investor likes to see. Buffett could be right: To really move on, Wells Fargo may need to steer clear of Wall Street.