The offer is an attempt by Redstone to resolve an impasse in the deal negotiations. Redstone has been trying to put together a deal that will keep Moonves, a 68-year-old media industry veteran credited with turning CBS around, at the helm, while positioning up-and-coming Bakish, 54, as Moonves' successor.
CBS shares rose 8 percent after Reuters first reported Redstone's offer, giving the company a market value of $20 billion. Viacom shares were up 5 percent, giving it a value of $12.6 billion.
Moonves has agreed to run the combined company for at least two years, as long as CBS Chief Operating Officer Joseph Ianniello will be president and chief operating officer of the combined company, so he can succeed him, sources have previously said.
Redstone, daughter of media mogul Sumner Redstone, has offered not to give Bakish any executive role in the combined company, but still wants him to sit on the board of directors and eventually succeed Moonves, the sources said on Friday.
Moonves does not want Bakish to be part of the combined company at all - either as an executive or board member - because he is seeking as much autonomy as possible in running the combined company, said one of the sources.
As a result of the impasse over Bakish's role, CBS executives have serious doubts that a deal will happen, the source said. CBS and Viacom have also disagreed about the stock exchange ratio that should be used in a merger, although the two sides are making progress on that front, the sources added.
The sources asked not to be identified because the matter is confidential. CBS, Viacom, and National Amusements Inc, the company of Shari Redstone, declined to comment.
Redstone offered her concessions earlier this week in a meeting with Moonves that included Richard Parsons, who recently joined the CBS board and is acting as a conduit between the two sides, the sources said.
There has not been any agreement about the composition of a combined company's board, the sources said.
Ten of the 14 director nominees for consideration at this year's CBS annual meeting are 70 or older. The average age is 72. The average for companies in the S&P 500 Index as a whole is 62. Two of Viacom's directors are 70 or older, according to the company's proxy statement.
REUNITING AFTER SPLIT?
CBS and Viacom set up special board committees to explore a merger in February, a move that would reunite the companies split by Sumner Redstone more than a decade ago. The merger would combine CBS's television network, local TV stations and Showtime cable network with Viacom’s cable networks, including MTV, Comedy Central and Nickelodeon, as well as its Paramount Pictures film studio.
CBS and Viacom also explored a merger in 2016, instigated again by the Redstone family, but those talks ended unsuccessfully, due to concerns by CBS about price and governance issues.
Since then, many of Viacom and CBS's competitors have combined, as scale becomes more important in the media business, with more customers cancelling pricey cable contracts and Netflix Inc and Amazon.com Inc spending billions of dollars on making shows and movies.
AT&T Inc is seeking to buy Time Warner Inc, pending a judge's ruling on a Department of Justice lawsuit to block the deal. Walt Disney Co announced in December it would buy the majority of Twenty-First Century Fox Inc assets. Discovery Communications recently acquired Scripps Networks Interactive Inc.
In their price negotiations, Viacom last month asked for 0.68 CBS shares for each Viacom class B share, the sources said at the time. CBS had offered 0.55 of its shares for each Viacom class B share, sources have said.
CBS reported first-quarter earnings on Thursday that topped revenue and profit estimates. Last month, Viacom reported better-than-expected quarterly profit and revenue.
"The strategy that we have laid out for you is clearly working and the good news is that there is much more to come," Moonves said on a call with analysts on Thursday.
(Reporting By Jessica Toonkel in New York; editing by Bill Rigby)
By Jessica Toonkel