I’ve spoken this week to multiple people who have at least discussed the possibility of running for office with Mr. Schultz and Mr. Iger. (All declined to be named discussing what were private conversations.)

Mr. Schultz, 63, with a fortune estimated by Forbes at $3 billion, came close to making a bid last year, but backed out after concluding it would be very difficult to defeat Mrs. Clinton, who seemed to have the Democratic nomination all but locked up and at the time seemed likely to win the presidency.

Those circumstances have obviously changed drastically. With Mr. Trump in office, the next Democratic race appears wide open, and many friends and potential donors are urging Mr. Schultz to run.

Mr. Schultz seemed to pave the way in December, when he announced he’d step down as Starbucks’ chief executive this April. But he continues to be actively involved in the expansion of the company’s high-end “roasteries” as well as its social-impact initiatives.

“Howard Schultz is definitely being pursued,” Mr. Gergen said. “He has a powerful social conscience. He comes from a very different place than the kind of chief executive with a big ego who wants the trappings of presidential power.”

Mr. Schultz declined to comment.

Last year Mr. Iger, 66, told The Hollywood Reporter that “a lot of people — a lot — have urged me to seek political office,” and last week the entertainment publication fueled renewed speculation when it reported that Mr. Iger had discussed the possibility with Mr. Bloomberg.

People who have discussed a possible presidential run with Mr. Iger told me that his discussion with Mr. Bloomberg, some years ago, focused more on a possible run for mayor of New York City, where Mr. Iger has an apartment. New York has long welcomed nonresident candidates like Mrs. Clinton, so Mr. Iger’s California residency isn’t seen as an obstacle.