The talks are expected to start in mid-June, CNBC reported on Thursday, citing sources. The companies have not yet held discussions, sources familiar with the companies said.
Both CBS and Viacom declined to comment.
Shares of Viacom rose 3.5% to close at $28.72, while CBS was up about 3.2% at $48.20.
The CBS board met on Wednesday to review strategic options that included an unofficial offer it made to buy Lions Gates Entertainment's Starz cable network for $5 billion, one source briefed on the meeting said.
As a condition of the September 2018 settlement that led to CBS dropping a lawsuit against its controlling shareholder, Shari Redstone and her family's National Amusement Inc, Redstone agreed not to raise the possibility of a merger between CBS and Viacom Inc, which she also controls, for about two years. But it left open the possibility of independent members of the CBS board proposing a combination.
Sources close the companies have said CBS' independent board of directors is reviewing a variety of options to protect itself against potential shareholder lawsuits that will likely come regardless of the outcome.
The widely anticipated third attempt to recombine CBS and Viacom is the latest in waves of media mergers to gird against competition for customers from digital rivals Netflix Inc, Amazon.com Inc and Apple Inc.
While big media companies Walt Disney Co, which purchased 21st Century Fox's entertainment assets, and AT&T Inc, which bought Time Warner, are tapping their extensive film and TV libraries to launch subscription streaming services, smaller players CBS and sister company Viacom have built advertising-supported and subscription video services while also providing original content to other distributors.
Reuters reported earlier in May that Lions Gates offered to sell cable channel Starz to CBS for $5.5 billion after rebuffing CBS' lower offer.
(Reporting by Kenneth Li in New York and Akanksha Rana in Bengaluru; Editing by James Emmanuel and Dan Grebler)