The media mogul Shari Redstone is in talks to sell a controlling stake in National Amusements, the parent company of the sprawling news and entertainment empire that includes the Paramount movie studio, CBS and MTV, according to three people familiar with the talks.

In recent weeks, National Amusements has held talks with Skydance, the media and entertainment company founded by David Ellison, who is the son of the billionaire founder of Oracle, Larry Ellison. It’s unclear whether a deal will be reached, and the value the talks place on Ms. Redstone’s stake couldn’t be determined.

A deal for Paramount, if it came to fruition, could be a starting gun for a far-reaching reordering of the media industry over the next year. Comcast, the TV and cable giant that owns NBCUniversal, is on the prowl for deals. Warner Bros. Discovery, the owner of HBO and CNN, in effect, comes on the market next year because of arcane tax reasons.

Ms. Redstone, 69, who waged a bitter battle with her onetime allies to retain control of the company, now appears to be seriously considering relinquishing it. She has held out for years amid broader headwinds facing the traditional media industry, but is exploring her options now that a serious suitor has expressed interest, two of the people said. Ms. Redstone’s holdings are facing some economic pressures, including long-term debt obligations and the unreliable advertising market for media companies like Paramount.

Puck earlier reported that Ms. Redstone and Skydance were in talks. Spokespeople for National Amusements, Ms. Redstone and Skydance declined to comment.

A deal for Ms. Redstone’s stake in National Amusements would represent a major changing of the guard in the media business. Paramount has been in the Redstone family for decades, since Ms. Redstone’s father, the bellicose deal maker Sumner Redstone, won the company in a hard-fought bidding war that drew heavyweights including the billionaire Barry Diller.

Paramount, with its bundle of cable channels, a movie studio and its CBS broadcast network, has long been considered an acquisition target. Ms. Redstone began holding conversations about a deal earlier this year with parties including technology firms like Amazon, Apple and Netflix, according to two people familiar with the matter.

The feverish deal making that seems poised to sweep the industry has partly been set off by the slow decline of television. For years, TV companies like Paramount were buoyed by ever-rising payments from cable distributors. But in recent years, the business model of cable TV has begun to collapse as consumers have dropped their cable subscriptions and shifted to streaming services like Netflix, leaving traditional television programmers looking for an exit.

Even streaming, once thought to be a savior of the media business, has begun to show signs of strain. Old-school TV companies like Paramount, NBCUniversal and Warner Bros. Discovery are pouring billions of dollars into building up streaming services in an attempt to catch Netflix, but none have so far managed to replicate the profits of cable TV.

Ms. Redstone is being advised by BDT & MSD Partners, a merchant bank founded by Byron Trott, a former Goldman Sachs partner who consults with some of America’s wealthiest and best-connected family business owners. Earlier this year, BDT & MSD Partners said it was taking a $125 million stake in National Amusements that would help the parent company pay down its loan obligations.

Ms. Redstone owns a controlling stake in National Amusements. In a February filing, Paramount said that National Amusements directly or indirectly owned about 77.4 percent of Paramount’s voting class A common stock.

Founded in 2010 by David Ellison, Skydance has emerged as one of the leading independent studios in Hollywood. It has a longstanding relationship with Paramount, producing hits like “Top Gun: Maverick” and “Mission: Impossible — Dead Reckoning.”

Skydance is backed by RedBird Capital Partners, a private equity firm that is among the most active in the media industry. RedBird is also backing RedBird IMI, the venture led by the former CNN chief Jeff Zucker that is pursuing a deal for the British newspapers The Telegraph and The Spectator.

Relinquishing Paramount would be a momentous step for Ms. Redstone, who fought to hold onto her family’s control as her father’s mental capacity began to decline. In 2018, CBS — led at the time by Les Moonves — sued Ms. Redstone to strip her control of her media holdings, but Ms. Redstone ultimately prevailed. Mr. Moonves, who faced a series of sexual harassment allegations, was ousted from CBS in 2018. He has denied allegations of nonconsensual sexual relations.

Though the value of Paramount has declined steadily in recent years — matching the broader fortunes of traditional media — investor speculation about a deal for National Amusements caused shares in the company to spike this month. Though its flagship streaming service, Paramount+, continues to lose money, Paramount said earlier this year that it had narrowed its losses for the service while continuing to add subscribers.

Rachel Abrams contributed reporting.