Shari and Sumner Redstone want Les Moonves to run a combined CBS Corp. and Viacom Inc., but they aren’t willing to offer him a stake or voting control of their family’s holding company, people familiar with the matter said.

The Redstones have said publicly that they won’t support a deal that requires them to give up control of CBS or Viacom. That includes surrendering voting control to Moonves, the chief executive officer of CBS, despite the Redstones’ respect for him, said the people, who asked not to be identified discussing private information.

The family will have to seek common ground over governance with Moonves to go through with its plan to merge the two media giants with him as CEO. Reviving faded Viacom networks like MTV and Comedy Central might be a tempting challenge for Moonves, 67. But he has run CBS with little interference and would want similar freedom if the companies are joined together, according to a person familiar with his thinking.

Moonves will probably want language in his contract similar to his current CBS agreement, which guarantees that independent directors remain and says he reports solely to the board and is the highest-ranking executive of the company, said another person familiar with the matter.

Moonves may seek provisions preventing the Redstones from unilaterally replacing board members and limiting the board’s authority, the person said. That could prevent situations like earlier this year, when National Amusements forbade the proposed sale of a stake in Viacom’s Paramount Pictures movie studio without unanimous board approval.

To retain Moonves, the Redstones should consider giving him control of their voting shares, said Mario Gabelli, whose funds are some of the largest shareholders in CBS and Viacom. That would give Moonves a degree of freedom to pursue the best path for the company, Gabelli said.

“If I were Les, I would ask for that,” Gabelli said in an interview.

Spokesmen for CBS, Viacom and the Redstones declined to comment.

The Redstones, whose National Amusements Inc. owns an 80 percent voting stake in both companies, asked CBS and Viacom late last month to explore a merger. That request is part of a series of moves spurred by Shari Redstone, who won a battle this year against former Viacom CEO Philippe Dauman to control the fate of Viacom. She has spearheaded changes at the company, asserting herself with her 93-year-old father Sumner in poor health.

The idea now is to revive Viacom, whose Paramount Pictures movie studio is also in disarray, by putting the company under the experienced hand of Moonves, who has helped CBS retain its lead as the most-watched U.S. TV network.