Murdoch Is Said to Want Iger to Stay as Disney C.E.O.

As part of 21st Century Fox’s sale talks, Rupert Murdoch has asked that Robert A. Iger extend his reign at Disney to oversee an integration of assets.

LOS ANGELES — Who will replace Robert A. Iger as chief executive of the Walt Disney Company when he retires in July 2019?

It could well be Robert A. Iger.

Disney is in talks to buy significant parts of 21st Century Fox, the media conglomerate controlled by the Murdoch family, and Rupert Murdoch has asked that any sale involve a commitment by Mr. Iger to extend his reign at Disney — for a fourth time — to help manage the absorption of Fox assets like the FX cable channel and the Star television operation in India.

The request, reported on Wednesday by The Wall Street Journal, was confirmed by two people briefed on the approach that Mr. Murdoch has taken in the talks, which they cautioned could still fall apart. They spoke on the condition of anonymity because the negotiations are confidential.

Speculation about who might succeed Mr. Iger, 66, has increased in recent weeks. On Tuesday, some news outlets had Mr. Murdoch’s son James, the chief executive of 21st Century Fox, as a likely candidate. Last week, Bloomberg reported that Bob Chapek, chairman of Walt Disney Parks and Resorts, could take Mr. Iger’s place.

In truth, Disney itself may not yet know for sure. The company has been conducting a search ever since an heir apparent, Thomas O. Staggs, stepped down as chief operating officer in April 2016. Disney said in March this year that Mr. Iger had agreed to remain chief executive until mid-2019, an extension of one year beyond his previously pushed-back retirement date. It has declined to discuss succession since then.

Hollywood has lately been of two minds about Mr. Iger. Some people close to him say he would like to run for political office, perhaps even president. Others believe that Disney’s board would like to have him push off his retirement yet again; Disney has its hands full even without a possible acquisition of 21st Century Fox assets.

In particular, Disney, which recently had one of its most senior executives, John Lasseter, take a six-month sabbatical because of behavior that made some staff members uncomfortable, is trying to turn its vast television business toward a streaming model. That effort involves the risky introduction of two Netflix-style services, one of which will not arrive until late 2019 — after Mr. Iger’s current retirement date.