Since Donald Trump was unexpectedly elected president on Nov. 8, 2016, speculation has swirled about whether another well-known business leader might make a bid for the White House in 2020.

Could that person be Howard Schultz?

Mr. Schultz, the chairman and former chief executive of Starbucks, said on Monday that he was stepping down from the company’s board. Though he did not announce a presidential bid, he acknowledged that he was considering entering politics.

“I intend to think about a range of options, and that could include public service,” he said. “But I’m a long way from making any decisions about the future.”

Although no chief executive has thus far undertaken a formal bid for the White House, and Mr. Trump’s victory may well prove an historical anomaly, many have been pegged as potential candidates, including Oprah Winfrey; Bob Iger, the chief executive of Disney; and Mark Cuban, the owner of the Dallas Mavericks.

“The history of business leaders in the White House has not been good,” said Prof. Douglas Brinkley, a presidential historian at Rice University and a CNN contributor. “You basically have Herbert Hoover and Donald Trump.”

Mr. Hoover, a mining executive who later served as commerce secretary under Warren Harding and Calvin Coolidge, presided over the start of the Great Depression. And Mr. Trump is among the most divisive presidents in American history.

“Because we had the Great Depression on Hoover’s watch, the feeling was that a businessperson in the White House was a disaster,” said Mr. Brinkley, who has written books about Franklin Delano Roosevelt, John F. Kennedy, Ronald Reagan and others. “And Trump was really a midlevel, self-employed C.E.O., not a real businessperson with a board of directors he was beholden to.”

Today, several factors are adding to speculation that someone from the upper ranks of corporate America might make a credible leader of the free world.

The election of Mr. Trump, a real estate developer and reality television personality, certainly opened that door of opportunity, making it clear that American voters were willing to elect a president with no prior government experience. (The last businessman without government experience to make a serious run at the presidency, Ross Perot, finished third in a three-man race in 1992 with 19 percent of the vote.)

American companies — including Starbucks — have become more political in recent years, wading into issues like immigration, gun rights and climate policy.

And at a moment when many voters say they are frustrated with partisan gridlock and ineffective government programs, some believe that an efficiency-minded business executive might bring some discipline and pragmatism to the Oval Office.

“There’s this notion that government is less effective than it should be, and that the cure could be a modern American business leader,” said Aaron Chatterji, a professor at the Duke University Fuqua School of Business. “There’s room for a natural outsider who is seen as making decisions based on benefits and costs, and less on ideology. That’s the theory at least.”

Mark Cuban, owner of the Dallas Mavericks and a co-host of “Shark Tank,” has said he was thinking about a presidential run in 2020.CreditMike Cohen for The New York Times

Mr. Schultz’s political aspirations are regarded with some skepticism among national Democrats, and it is unclear whether there is any popular constituency in the party for a wealthy white businessman who lacks government experience. But Mr. Schultz has repeatedly expressed interest in the presidency to his associates, and of the numerous political outsiders flirting with a 2020 campaign, he is seen as being among the more serious in his ambitions.

Mr. Schultz bought Starbucks in 1987 and turned it into one of the most successful restaurant chains in the world. Over the years, he has spoken out on issues including gun violence, gay marriage and race relations, often using Starbucks to make political points. Last week, the company shut down most of its locations to conduct anti-bias training after the arrest of two black men at one of its stores in Philadelphia.

Mr. Schultz has also built something of a political network while leading Starbucks, working closely with the public-relations firm Edelman — where John McCain’s former campaign manager, Steve Schmidt, is a top executive — and the Democratic consulting group SKDKnickerbocker, which is stocked with former advisers to politicians like Hillary Clinton and Michael R. Bloomberg. A donor to Democrats, Mr. Schultz has also shown interest in centrist political organizing and hosted a town hall for the nonpartisan group No Labels in 2011.

And Mr. Schultz, 64, has another thing going for him: money. He is worth an estimated $2.8 billion, according to Forbes.

“It costs a billion dollars to run for president today,” said Mr. Brinkley, adding that Mr. Perot proved in 1992 that “you don’t even have to campaign very hard, you just had to spend money.”

Mr. Schultz is not alone in having deep pockets, of course. Mr. Cuban, the billionaire owner of the Dallas Mavericks basketball team and a co-host of “Shark Tank,” is another outspoken critic of President Trump who has flirted with a presidential run.

When asked on Monday if he had given any more thought to a presidential bid, Mr. Cuban emailed, “Yes. But not willing to discuss at this point.”

And Ms. Winfrey, who is worth an estimated $2.9 billion, created a stir in January after she delivered a stirring speech at the Golden Globes that sounded to many like a presidential trial balloon.

Since then, Ms. Winfrey’s camp has offered mixed signals about her intentions. A representative for Ms. Winfrey declined to comment on Monday.

Other big-name executives have effectively taken themselves out of the running.

Mr. Iger seemed to be seriously entertaining the notion. But Disney’s pending acquisition of a number of 21st Century Fox assets is contingent on his remaining chief executive for several more years, and he has signaled that he plans to remain at the company.

Jamie Dimon, the chief of JPMorgan Chase, has been put forward as another potential presidential candidate who could appeal to voters with a mix of pragmatism, business success and charm. But in recent months Mr. Dimon has ruled out a presidential run, according to a person familiar with his thinking.

And Mark Zuckerberg, Facebook’s chief executive, last year crisscrossed the country on a listening tour that looked much like a political campaign, but has offered no indication that he is seriously considering a run

In recent years, other prominent business leaders have fallen short in their efforts to reach the White House. Mitt Romney came from a political family and served as governor of Massachusetts. Running largely on his experience as a private equity executive, he won the Republican nomination in 2012, but lost to President Barack Obama.