Dish Network Corp. is in talks to merge with T-Mobile US Inc., people familiar with the matter said, a deal that would accelerate a wave of consolidation across the U.S. media and communications industries.

The two sides are in close agreement about what the combined company would look like, with Dish Chief Executive Charlie Ergen becoming the company's chairman and his T-Mobile counterpart, John Legere, serving as the combined company's CEO, the people said.

Tougher questions about a purchase price and the mix of cash and stock that would be used to pay for a deal remain unresolved, the people said. One of the people characterized the talks as at "the formative stage," and said an agreement might not ultimately be hammered out.

If completed, the deal would be the latest multibillion-dollar combination in traditional television and communications industries being upended by the Internet. T-Mobile rival AT&T Inc. is close to wrapping up its $49 billion deal for Dish rival DirecTV that will create the country's largest pay-TV company. Meanwhile, Charter Communications Inc. recently announced a total of $67 billion in deals that would roll up Time Warner Cable and Bright House Networks to create the second-largest U.S. cable operator.

A deal would likely be very large. T-Mobile has a market capitalization of about $31 billion, a little below Dish's $33 billion.

A Dish deal with T-Mobile would combine the country's second-largest satellite TV operator with its fourth-largest wireless carrier. It would also address major strategic issues for both sides.

Dish lacks the robust broadband Internet service that cable companies can lean on to offset a declining TV business. It also has amassed billions of dollars of wireless licenses but hasn't built the cellular network needed to put them to use. T-Mobile's wireless service would help address both needs.

T-Mobile, meanwhile, has added subscribers at an industry-leading rate over the past several quarters, but still is dwarfed by much bigger rivals AT&T and Verizon Communications Inc. Dish's wireless licenses would give T-Mobile a path to boosting the capacity of its network.

T-Mobile has about 44.7 million retail customers, which includes mainstream and prepaid customers. Dish has 13.8 million satellite TV customers and 591,000 Internet subscribers.

Deutsche Telekom owns 66% of T-Mobile and has for several years been looking to either sell the company or merge it with another.

One significant uncertainty is Mr. Ergen, who has held talks with companies across the wireless and satellite industries in recent years without completing a major deal. Dish bid openly--and unsuccessfully--for wireless carriers Sprint Corp. and Clearwire Corp. two years ago and has earned a reputation as a deal maker who is tough to get to closing.

Still, Dish has consistently expressed interest in entering the wireless industry. It has been amassing licenses to use wireless airwaves for several years. Earlier this year, it worked with two smaller firms to bid $13.3 billion in a government auction of wireless airwaves, second only to AT&T's $18.2 billion.

T-Mobile has transformed itself from the weakling of the wireless industry into its fastest-growing carrier. Under Mr. Legere, T-Mobile acquired regional rival MetroPCS in 2013, made strides in improving the quality of T-Mobile's network, and was the first carrier to do away with two-year contracts. It also began paying subscribers to switch carriers and soon began adding customers at a rapid clip. In the first three months of the year, it was the only major U.S. carrier to add phone customers, and T-Mobile is now on track to pass rival Sprint and become the country's third-largest wireless carrier by subscribers.

T-Mobile spent much of last year in talks to be acquired by Sprint. Those talks fell apart after federal regulators--insistent on preserving four national wireless carriers--repeatedly signaled they would block a deal.

That opened the door for Mr. Ergen. In May, Mr. Ergen said, "We admire what John and his team have done at T-Mobile," referring to Mr. Legere, the CEO, "and certainly we follow what they do."

A T-Mobile deal with Dish could face far less opposition from regulators, because the companies are in different industries and because a deal could in theory create a stronger wireless competitor. AT&T's similar combination with DirecTV is expected to be approved. Regulators would look to see if the combined companies might need to shed some spectrum, however.

On Tuesday, Mr. Ergen uncharacteristically agreed to sit down with analysts and investors for a meeting in the Denver area near Dish's headquarters. While much was expected of the meeting, analysts and investors said they came away with little additional insight about Dish's wireless plans. "Some attendees were clearly disappointed that there were no announcements," J.P. Morgan analyst Phil Cusick said in a research note Wednesday.

Mr. Ergen reiterated in the meeting that Dish has four options for its wireless strategy: join with another company to offer wireless service, sell Dish's spectrum or the whole company, acquire another company with a network, or wholesale the spectrum. Analysts said Dish made clear it has no plans to build a wireless network from scratch.

Mr. Cusick said Dish's view is that "spectrum values should increase as bandwidth shortages crop up, so Dish has no urgency to act, but again is open to the right near-term deal if it comes along."

Write to Ryan Knutson at ryan.knutson@wsj.com, Thomas Gryta at thomas.gryta@wsj.com and Shalini Ramachandran at shalini.ramachandran@wsj.com

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