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David Letterman to Katie Couric: 'You Can't Leave' CBS (Video)

Katie Couric on The Late Show
JP Filo/CBS

He tells her to "saddle up and…ride into the sunset," at the "Evening News."

David Letterman wants Katie Couric to stay at CBS as host of the Evening News, even though her $15 million contract is up in June.

When asked if she'll leave, Couric told Letterman on the Late Show Tuesday, "I have no idea actually." The Hollywood Reporter has reported that she's considering a daytime show with her former boss, Jeff Zucker.

"So that means, theoretically, you could actually leave the network? You can't leave the network, could you?" Letterman replied.

"I'm figuring out what I want to do," Couric said. "I'm in the process of figuring it out."

"Once you take the anchor chair, that's what you do," Letterman responded. "It's not like a temporary gig."

Couric defended herself: "Five years isn't too temporary."

Letterman pointed to Walter Cronkite, Tom Brokaw and Peter Jennings, who served as anchors for years.

"They get in, they saddle up and they ride into the sunset. Into the sunset!" he said.

Said Couric, "I love doing the Evening News. I'm really proud of it."

Still, Letterman insisted, "You can't leave. There's a period of adjustment to get accustomed . . . to build up faith in the character of the person presenting the news."

"OK. OK, Dave," Couric said.