One of Discovery Communications’ big selling points: its Shark Week programming. (The Washington Post)

Discovery Communications and Scripps Networks shares climbed Wednesday on reports that the companies are considering a merger as they grapple with a rapidly changing media landscape in the Internet era.

Shares of Silver Spring, Md.-based Discovery closed up 4.3 percent in trading Wednesday. Knoxville, Tenn.-based Scripps Networks soared 14.7 percent.

The combination would create a video content producer with $10 billion in revenue, a sprawling global reach, and greater leverage with cable and Internet firms.

The companies have flirted with linking up before. It is not clear whether the two will combine and what form it might take.

Although both companies declined to comment, Discovery chief executive David Zaslav, one of the highest-paid public company executives, told CNBC on Tuesday that media companies needed to “disrupt” themselves to maintain relevance and reward shareholders.

His comments came as video-on-demand juggernaut Netflix this week reported 5.2 million total memberships in its latest quarter, boosting its share price 10 percent.

“We have a choice,” Zaslav told CNBC’s “Squawk Box.” “We can hold on to our existing business or try and do some of these new forms of content. Or we can figure out how to disrupt ourselves. We want to become relevant on all platforms.”

News of the talks follows Allen & Co.’s annual meeting of media and tech moguls in Sun Valley, Idaho, last week, the starting point for many past media deals.

Some analysts were positive about the prospect of a merger, which several see as a smart move because the companies need the scale and digital chops to negotiate with distributors in today’s fast-moving media world.

“We view the deal as among the most logical in media,” RBC Capital Markets analyst Steven Cahall said in a report. “While their combination may not put them on equal footing with a broadcast network or major sports rights owner, scale matters and should improve network carriage and affiliate negotiations.”

It's a combination that promises something for everyone.

Discovery is known for its ­testosterone-driven, over-the-top programming such as Shark Week, which this year will include a race between Olympian Michael Phelps and a great white, and its man-vs.-nature shows such as “Deadliest Catch” and “Bering Sea Gold,” about prospecting for gold in the frigid waters off Alaska.

Scripps Networks offers a portfolio of shows that appeal to the lucrative female demographic, including those in the do-it-yourself genre featured on the Food Network, HGTV, the Travel Channel and the Cooking Channel.

Discovery is also known for its rigid cost discipline and massive international footprint — 2.8 billion viewers in 200 countries and 40 languages — that would complement Scripps Networks’ nascent global distribution.

Cahall and a report from Morgan Stanley’s Benjamin Swinburne emphasized the cost savings that the pairing could bring. Swinburne estimated that it could be $300 million to $500 million (or 10 to 15 percent of Scripps Networks’ 2016 revenue) by reducing duplicative overhead costs and key support areas such as ad sales.

Swinburne issued a report Wednesday noting that greater scale makes more sense in the cable industry because of increasing uncertainty over distribution channels and slower advertising growth in the age of Facebook, Google and Amazon. Finally, Swinburne said, low borrowing costs make acquisitions timely.

Discovery has a market capitalization of $11.4 billion. It has more than $6 billion in annual sales and 7,000 employees.

Both companies have strong balance sheets. Each produces net profit margins in the high teens, with Discovery earning a net profit of $1.2 billion last year. Scripps Networks’ net profit was $673 million. It has 3,600 employees. Its shares have been on a tear in recent years, nearly doubling since pre-financial-crisis days.

Scripps Networks Interactive was spun out of the longtime Cincinnati-based newspaper chain and media service E.W. Scripps Co. in 2008.

Advance Publications, the privately held media company owned by the Newhouse family, owns a large share of Discovery stock.