The companies said in separate statements Thursday that their boards have formed exploratory committees to mull a deal. Viacom said it has hired outside legal advisers and will hire bankers.
Statements from both companies said, "There can be no assurance that this process will result in a transaction or on what terms any transaction may occur." They also said they wouldn't comment further, "until the process is completed."
A combination of the two, which were split more than a decade ago by the media mogul Sumner Redstone, is being orchestrated by his daughter Shari. It would combine CBS's broadcast television network with Viacom's cable channels and film studio amid a big shakeup in the industry.
The Redstones control both CBS, which has a market value of $22 billion, and Viacom, $13 billion, through their privately held National Amusements. An earlier effort to combine the two was abandoned a little more than a year ago.
In its own statement, National Amusements said it "supports the processes announced by CBS and Viacom to evaluate a combination of the two companies, which we believe has the potential to drive significant, long-term shareholder value. National Amusements does not currently intend to make any further comments regarding the process."
CBS shares rose 2.2 percent on Thursday, while shares of Viacom closed down 0.6 percent.