By Dana Mattioli and Dana Cimilluca, Dow Jones Newswires

CenturyLink Inc. is in advanced talks to merge with Level 3 Communications Inc., a deal that would give the business-telecommunications companies greater heft in a brutally competitive industry.

A deal could be announced in the coming weeks, according to people familiar with the matter. As always, there is a possibility the talks could fall apart.

Terms of the deal couldn’t be learned. As of Thursday afternoon before the Journal’s report of the talks, Broomfield-based Level 3 had a market value of $16.8 billion. CenturyLink, based in Monroe, La., was worth $15.2 billion.

Shares in Level 3 were up 11 percent at $52.28, while CenturyLink shares were up 8.3 percent at $30.58 on Thursday afternoon after the Journal’s report.

CenturyLink gets about two-thirds of its revenue from business customers, while Level 3’s comes entirely from that segment.

Level 3, which traditionally focused on so-called enterprise customers, was one of the biggest telecom operators to survive the dot-com bust. The company runs one of the largest internet backbones in the world but has turned its focus increasingly to small and midsize business in an attempt to reverse slowing sales growth in its core business.

Year to date, the company’s stock had fallen more than 14 percent before the talks were reported. Singapore state investment firm Temasek Holdings Pte. Ltd. is Level 3’s largest shareholder, with 18 percent of its stock, according to FactSet. Level 3 is scheduled to report third-quarter earnings next week.

CenturyLink, traditionally a rural local-phone-service provider, has sought to upgrade its network with fiber-optic lines in a bid to compete with AT&T Inc., Verizon Communications Inc. and rivals in the cable industry. The company has also branched into hosting and cloud services, though lately it has been looking to sell some of its data centers. CenturyLink operates more than 55 data centers, according to its website.

The so-called wireline business of running telephone and internet lines has suffered from brutal competition over the past 15 years, hurt by plummeting prices for network bandwidth and high capital costs.

The possible deal also illustrates both companies’ dwindling acquisition opportunities in the sector after years of consolidation.

Both companies have historically been acquisitive. In 2014, Level 3 bought TW Telecom for about $6 billion. In 2011, it bought rival Global Crossing Ltd. for roughly $2 billion.

CenturyLink, formerly called CenturyTel, has also been a voracious acquirer. In 2011, it bought Qwest Communications International for $11 billion and Savvis Inc. for about $2 billion, two years after it purchased Embarq Corp. for about $6 billion.

There has been a wave of deal making among technology, media and telecom companies in the past couple years, with more than $750 billion struck globally just this year, according to Dealogic. While that lags behind the tally up to this point last year, which represented a high mark for mergers and acquisitions across the board, it is more than in any other year since 2000.

On Thursday, semiconductor company Qualcomm Inc. agreed to buy NXP Semiconductors NV in a $39 billion deal. It is the largest chip merger to date and the second-largest marriage of technology companies, after Dell Inc.’s recent acquisition of EMC Corp. for $67 billion.

Overall deal volume is down from last year, but the gap is closing as a number of blockbusters have been agreed to in the past week, including AT&T Inc.’s $85 billion plan to buy Time Warner Inc.

Drew FitzGerald contributed to this article.