Shares of both Viacom Inc. and CBS Corp. rose noticeably Friday after a new report suggested the two companies, both controlled by the Redstone family, could once again be considering the prospect of merging.

A report in The Wrap suggested Shari Redstone, president of the family’s National Amusements movie-theater chain, had recently sparked new discussions within the companies about a possible merger. Her father, Sumner Redstone, had combined CBS and Viacom in 2000, only to pull them apart six years later. National Amusements in September of 2016 formally requested that the boards of both companies consider the possibility of a new merger on an all-stock basis, then stopped the process at the end of that year.

CBS declined to comment. A Viacom spokesman did not immediately respond to a query seeking comment.

The report comes as more media companies are considering tie-ups that would give them a larger footprint in a sector that has been flummoxed by new technology and consumer patterns. Monetizing viewership of content has become more difficult as consumers migrate to new video screens and behaviors that aren’t measured as easily, crimping the flow of advertising support and undermining media companies’ ability to lock in fees from distributors.

To fight back against these trends, a number of prominent media companies have set big acquisitions or outright mergers. Among the recent combinations: Charter Communications and Time Warner Cable and Lionsgate and Starz. Other tie-ups have been proposed but not completed. Discovery Communications is expected to finalize its purchase of Scripps Networks Interactive later this year. AT&T is pursuing legal options to finalize its proposed merger with Time Warner. And Walt Disney has agreed to purchase a substantial chunk of 21st Century Fox, including the 20th Century Fox movie studio, the FX and National Geographic cable networks and a passel of regional sports operations.

The companies that don’t embrace other assets have begun to look considerably smaller.

If a merger is being discussed, it is not on a fast track. A person familiar with the situation suggested no substantive steps in any process were taking place at the current time.

Viacom shares reacted quickly to the news. Shares of the company, which controls MTV, Nickelodeon, Comedy Central and the Paramount movie studio, rose nearly 10% Friday, or $2.95 a share, to $33.76 a share from $30.90. Volume was strong – 12.45 million shares – compared to average volume of 5.07 million.

Shares of CBS rose more modestly, up 1.85%, or $1.07 a share, to $58.83 a share from $57.78. Volume was 6.19 million compared with average volume of 4.01 million.

CBS has fared well in recent months, despite its medium size in the sector. The owner of the CBS broadcast network and the Showtime cable outlet has in recent months focused on maximizing the revenue it draws from its content by scrutinizing the fees it draws from retransmission and overseas syndication. Rather than make big acquisitions, CBS has launched a spate of new digital businesses, including the “CBS All Access” subscription video on demand service and a streaming-video news product, CBSN, that makes new use of content from CBS News. Leslie Moonves, the company’s chairman and CEO, has discussed the launch of a new streaming-video sports-content service and CBS has unveiled interesting plans for “All Access,” like a revival of the classic series, “The Twilight Zone.”

Viacom, meanwhile, has worked to recalibrate itself under a new leader. Bob Bakish took over as CEO of the company in December of 2016 and has since that time reorganized the company and placed new leaders in charge of MTV and set about to transform the company’s Spike cable outlet into a more general-entertainment property called the Paramount Network. A launch is slated in the days ahead. Bakish has also placed more emphasis on events related to some of the company’s big assets, including a new festival launched by Comedy Central.