Wall Street Journal reports that CBS directors met last week when they discussed a potential deal. If talks proceed it would be the third attempt to bring the two companies together since their division by Sumner Redstone 13 years ago.
It follows a pattern that has seen leading players Time Warner, NBCUniversal, Discovery and Scripps Networks all participate in a series of mergers and acquisitions.
Viacom Chief Executive Bob Bakish is said to be a shoo-in to take the leadership position in any combined company, however the Journal says there is debate over who would fill the remaining management roles.
Viacom has emerged as the poorer of the two channels, having suffered under the US trend towards cord cutting. However, it would bring CBS the younger demographic of MTV and CBS.
CBS meanwhile has benefitted from sports and broadcast TV success. But its boardroom has seen the departure of chief executive Leslie Moonves amid allegations of sexual assault and harassment, which he denies.