Other investments have eluded that Midas touch. Ms. Winfrey’s cable channel, OWN: The Oprah Winfrey Network, a joint venture with Discovery Communications Inc., initially struggled to gain traction and last year earned an average of 462,000 prime time viewers daily. In December, Discovery said it would take majority control of OWN, purchasing 24.5 percent of the channel for $70 million from Ms. Winfrey’s company, Harpo.

Ms. Winfrey’s most potent appeal, industry analysts say, is among somewhat older consumers — or perhaps, voters — with women over 55 as her strongest cohort. She is especially popular among African-American women and white suburban women, two groups Democrats will rely on in the 2018 and 2020 elections.

By Monday afternoon, the White House had responded to the threat of Oprah in 2020. “We welcome the challenge,” said Hogan Gidley, a spokesman for the president, “whether it be Oprah Winfrey or anybody else.”

But Ms. Winfrey has approached politics cautiously over the years, engaging highly selectively. In 2007, she intervened for Mr. Obama, holding rallies for him and hailing him as “the one.” And in 2013, she hosted a fund-raising event for Cory Booker, in his first bid for Senate in New Jersey.

During the 2016 campaign, Ms. Winfrey endorsed Mrs. Clinton but never ventured onto the campaign trail. Though Ms. Winfrey and her staff discussed a possible appearance with the Clinton campaign, none was ever scheduled. Ms. Winfrey’s aides cited her focus on righting her television network as the reason for her difficult schedule.

Minyon Moore, a Clinton adviser who communicated with the Winfrey team, said the campaign had been “delighted” to have Ms. Winfrey’s endorsement. Should Ms. Winfrey seek to assemble a campaign team for 2020, Ms. Moore said, “I suspect she would have her pick.”

Less certain is whether Ms. Winfrey could navigate the ideological pitfalls of a presidential campaign and give voice not just to broad themes, but actual policy prescriptions. While Ms. Winfrey has aligned herself generally with Democrats like Mr. Obama, her views on a range of issues from financial regulation to drone warfare are opaque. She drew criticism from the left last year after saying in an interview that she felt hopeful and believed Mr. Trump had been “humbled” after meeting with Mr. Obama during the presidential transition.