After Page Six reported that there was a brouhaha over “CBS This Morning” failing to get a Bob Woodward book exclusive this week, we’re told that the same problem has been the source of intrigue and envy at the network “for years.”

Insiders were irked that Woodward did his first interview about blockbuster book “Rage” with rival morning show “Today” — even though it was published by CBS sister company Simon & Schuster, which are both owned by Viacom.

Now sources tell us that in recent years there have also been battles over Hillary Clinton’s 2017 election autopsy, “What Happened,” and Woodward’s previous scorcher, 2018’s “Fear” — both of which saw big live interviews go to rival networks, usually after a taped spot aired on CBS. Even Michelle Obama — whose memoir “Becoming” was a publishing phenomenon — sat down with ABC’s Robin Roberts before CBS’s Gayle King.

One exasperated insider said, “Management can’t get the [CBS] shows to all work together to use their collective leverage to help the morning show be more competitive.”

They lamented that “NBC would never let this happen, or ABC.” They added that on a memorable recent occasion, “CBS Sunday Morning” bagged the Clinton exclusive — then wouldn’t cough up footage for “CBS This Morning,” fearing it would diminish their exclusive.

“[It] became a big internal battle,” the insider said.

Meanwhile, an insider argued that it’s not an apples-to-apples comparison: ABC doesn’t have a rival to “60 Minutes,” and CBS News has become “even more collaborative” since new management took over in early 2019 and overhauled that division.

A rep for CBS said: “CBS News books top authors all the time and every show benefits from that win.”