Iger, 66, had said he would retire from the company he has steered through a rapid expansion when his deal expires in July 2019.
But the sale of Fox assets probably would face a lengthy regulatory review, meaning the transaction probably wouldn't close for at least another year.
For that reason, the Disney board is expected to extend Iger's contract so that he can oversee the integration of Fox properties with Disney, according to a person familiar with the matter who was not authorized to speak publicly.
However, Iger has not extended his contract yet, and Disney may not buy Fox, which also is considering bids from other companies, including
A Disney spokeswoman declined to comment.
Analysts said they would not be surprised to see Iger stay on the job a few more years.
"This is exactly what Disney would need — a great integrator of business units following a merger," said C. Kerry Fields, a professor of business law and ethics at the USC Marshall School of Business. "It provides stability to the management teams on both sides of the transaction. Having an experienced hand following an acquisition is crucial to ensure that the merged-in company will fit the culture and opportunities of the acquirer."
The Wall Street Journal first reported that Iger would probably stay past 2019 in the event of a Fox acquisition.
Disney is in high-level talks to buy Fox properties including the 20th Century Fox film and television studio in Los Angeles, which is responsible for movies including "X-Men" and "Deadpool" and TV shows such as "This Is Us."
Along with the studio, Disney would buy Fox cable channels, including FX and National Geographic, and its international holdings, which include a stake in the European pay-TV service Sky and operations in India and Latin America, according to people familiar with the discussions.
Insiders have said a deal could give Fox Chief Executive
Since he became CEO in 2005, Iger's contract has been extended three times amid a protracted search for a successor. Thomas Staggs, Iger's former heir apparent, left Disney's No. 2 post last year after Disney's board privately expressed a lack of confidence in him — throwing carefully orchestrated succession plans into question.
In March, Disney announced Iger's contract would be extended until mid-2019 — he was previously set to leave about a year earlier — giving the company more time to find someone to fill his role. But with few obvious internal candidates, the board seems increasingly likely to look outside Disney for its next CEO.
In October, Iger reiterated his retirement plans at Vanity Fair's new establishment summit in Beverly Hills.
"This time I mean it," Iger said at the event.
Many people have speculated that Iger, who has been outspoken on issues such as gun control and climate change, may seek public office after he leaves Disney.
But investors have been reluctant to see him leave. Iger has overseen a successful transformation of Disney through big-ticket acquisitions that paid off handsomely — sending the company's stock soaring.
During his tenure, Disney has been enhanced by the purchases of Pixar Animation Studios, Marvel Entertainment and Lucasfilm, each of which has given the company powerful franchises to exploit across its various businesses, including film, TV, toys and theme parks.
Disney's shares fell $1.76, or 1.6%, to $105.46 in Wednesday trading. Fox shares rose 22 cents, or less than 1%, ,to $33.21.
Times Staff Writer Daniel Miller contributed to this report.
3:45 p.m.: This article has been updated with additional information about Disney and Robert Iger's succession planning, and a quote from a USC professor.