A letter released by Sumner Redstone and his daughter Shari Redstone said the boards of the two firms should consider bringing together the firms that broke up in 2005.
The 93-year-old Redstone, who is believed to be in failing health, remains chief executive of the holding company National Amusements, the controlling shareholder of the two firms. Shari Redstone is president of the group.
"We believe that a combination of CBS and Viacom might offer substantial synergies that would allow the combined company to respond even more aggressively and effectively to the challenges of the changing entertainment and media landscape," the letter said.
The letter said Sumner and Shari Redstone would not participate in board deliberations on the proposal.
The proposed merger aims to end a melodrama over control of Sumner Redstone's empire which has seen a series of lawsuits and upheaval at the top ranks of Viacom.
Viacom, which owns Nickelodeon, MTV and other networks, said last week it would shelve a proposal to divest its Paramount studio, and that interim chief executive Tom Dooley was stepping down.
The merger would bring together Viacom with CBS, which owns an array of television and online assets.
Viacom said in a statement it had received the letter and would likely create a committee of independent shareholders to evaluate the proposal.
Analysts have said the two firms need to shift their focus to better compete with rising media starts such as Netflix, Hulu and Amazon.
One potential scenario envisioned by analysts would see CBS chairman and chief executive Les Moonves take over the combined firm.
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