Harvey Schwartz, president and co-chief operating officer of the Goldman Sachs Group Inc.

Andrew Harrer | Bloomberg | Getty Images

Harvey Schwartz, president and co-chief operating officer of the Goldman Sachs Group Inc.

In contrast, former chief financial officer Schwartz spends more of his free time at the office, according to a New York Times article in late November.

“Over five hours of interviews for this article, the most revealing moment about his business psychology came when he described how he interviews job candidates: He asks them to try to sell him the Polycom speakerphone that sits on his desk,” the Times said.

Schwartz was Goldman’s chief financial officer for four years. He is a former nightclub bouncer and started out in finance after college. Schwartz eventually made his way to a job at J. Aron, the Goldman commodities unit that was also the launch pad for Blankfein’s career at the bank.

Looking at Goldman’s history of executives, it’s possible Solomon and Schwartz could lead the bank together after Blankfein leaves.

“There had always been a co-CEO model at Goldman Sachs before Lloyd Blankfein, so I’m not sure Goldman would go back to one CEO when he leaves,” said Ken Leon, bank analyst at CFRA. “I’d be surprised if the company picked one CEO when Blankfein leaves.”

Blankfein has not ruled out the possibility of Solomon and Schwartz taking the reins together.

“Goldman Sachs as a firm has a long tradition of co-CEOs,” Blankfein said in an interview with Bloomberg in late November. “That can work if it works and people get along, but it doesn’t necessarily have to work. So I would say that it’s not a guarantee.”

Jon Corzine and Hank Paulson shared the CEO title in the late 1990s. Corzine left in 1999, eventually becoming governor of New Jersey. Paulson would hang on as CEO until 2006, when he left to become treasury secretary for the Bush White House.

— CNBC’s Fred Imbert and Liz Moyer contributed to this report.