“CBS Mornings” star Gayle King is “not happy” that Norah O’Donnell could return to co-anchor the struggling show — even as Editor-in-Chief Bari Weiss weighs a possible “Morning Joe”-style overhaul of the broadcast, The Post has learned.

A source said King was upset over new promos for the show that included O’Donnell, who has been substituting periodically, as Weiss and News President Tom Cibrowski look to replace Tony Dokoupil, who decamped for “CBS Evening News” earlier this year.

“Gayle was not happy,” the source said. “She does not want Norah to return to the show.”

Another source described King and O’Donnell as cordial colleagues bordering on “frenemies,” and cited the duo’s strained relationship when they co-anchored the network’s morning show from 2012 to 2019.

“Gayle is an authentic person. She loves the news,” the person said. “Norah loves the idea of being on the news.”

A network source stressed that King is central to “the process of finding a new co-host,” and that “nothing will happen without her blessing.”

While O’Donnell isn’t yet a shoe-in for the empty slot, she has been long rumored to be a leading candidate, as first reported by The Post in February. Other contenders include Eva Pilgrim, Elisabeth Hasselbeck and CBS News anchor Kelly O’Grady, Status reported.

Aside from naming a third anchor, two sources told The Post that Weiss plans to relaunch “CBS Mornings” and has been mulling modeling the program after MSNow’s “Morning Joe,” which mixes opinion and commentary on current events.

While no drastic overhaul is expected this fall, Cibrowski and Jon Tower, the interim executive producer of “CBS Mornings,” are hoping to name a permanent co-host as soon as September, along with some programming tweaks to start, according to a source with knowledge.

“Tom is telling people that it’s going to be more of a live show with fewer people and Jon is saying he wants it to be more loose like ‘Morning Joe,’” an insider said.

The person added that they expect the show to be more “chat-driven in the vein of ‘Morning Joe,’” pointing to Tower’s past working on the Joe Scarborough and Mika Brzezinski-helmed program.

The person noted that instead of a single news segment with eight to nine short news stories, the hosts will delve into topics more deeply.

“The show is f–ked. They need to try something!” the person said, citing the show’s recent historic ratings lows, when it dropped to 1.59 million total viewers the week of July 13.

CBS News declined to comment.

A network source said a “Morning Joe-style” format has been discussed internally but denied that the revamp will include such a drastic change.

The ambitious O’Donnell — whose career had stalled under the previous CBS News boss — has lately seen her prospects improve under Weiss, who took the helm last October.

After being ousted as anchor of “CBS Evening News,” O’Donnell went from being a mere senior correspondent to grabbing a plum correspondent job on “60 Minutes,” a new podcast — and potentially returning to the morning show, which she once co-anchored with King and Charlie Rose.

While some insiders griped that O’Donnell won’t move the ratings needle much, the journalist’s political reporting chops and polish could help the last-place “CBS Mornings.”

Rumors of Weiss’ plans to overhaul the broadcast are sparking anxiety inside the halls of CBS News.

“She’s going to turn the morning show into a podcast,” said one miffed insider, who noted that the show lacks an “intellectual” to make sense of the day’s news.

The person added that this is not the strength of King and co-host Nate Burleson. Even O’Donnell, who has a strong news reporting background, isn’t known for unspooling her opinions on current events.

Another CBS insider noted that it’s possible that Weiss taps others at the network to take part in analysis.

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