Until last week, most analysts believed that the Murdochs had no interest in selling any component of 21st Century Fox. In fact, attention recently has focused on their efforts to make it larger: James Murdoch, the chief executive of 21st Century Fox, has been trying to gain regulatory approval to buy control of Sky, the European satellite behemoth.

But certain 21st Century Fox holdings became in play on Nov. 6, when acquisition talks with Disney were disclosed. Disney was also interested in buying the company’s overseas assets — along with the minority stake that 21st Century already owns in Sky, there is the sprawling Star India television and digital business — and certain operations in the United States, including the Fox movie studio, which includes Fox Searchlight, and a share of Hulu, the streaming service.

Disney and Fox are no longer talking, for now.

Verizon had expressed preliminary interest, according to people briefed on the matter, though one of them added that the company is not currently interested in pursuing a deal.

This is all happening as the traditional media industry scrambles to contend with a struggling film business and sputtering cable networks, which have been buffeted by viewership declines and subscriber erosion. At the same time, streaming services like Netflix are surging and tech giants like Apple have arrived in Hollywood.

To compete, big players like the Walt Disney Company and Comcast have been looking to get even bigger. (Disney recently paid $2.5 billion for BamTech, a video streaming company, and said it would introduce a pair of Netflix-style streaming services.) Small conglomerates like Discovery and Scripps Media have sought refuge in each other’s arms.