01/07/2013 10:04 am ET Updated Jan 08, 2013

Letterman Tells Oprah How He Lost 'Tonight Show' To Leno (VIDEO)

In 1991, 30 years after legendary comedian Johnny Carson started hosting "The Tonight Show," rumors began swirling that he was retiring. The news sparked a battle for Carson’s seat between two comedians: Jay Leno and David Letterman. Then, just days before Carson confirmed that he was indeed stepping down, NBC announced that the coveted spot would go to Leno.

Letterman went on to strike a multimillion-dollar deal with CBS for a new show, "Late Show with David Letterman," which would air opposite "The Tonight Show." For the past 20 years, the two late-night rivals have gone head-to-head in the ratings.

Now, during an interview with Oprah Winfrey for "Oprah’s Next Chapter," Letterman reveals why he'd thought that he was going to be the retiring Carson’s heir apparent.

He tells Oprah in this clip that before Leno landed "The Tonight Show" gig, he himself had two meetings with NBC executives. “They said, ‘We want you to take Johnny's job. We just want to make sure that you're interested in this,’” he says.

After the second meeting, Letterman says, he asked if they’d mentioned their plans to Carson -- a man he considered a mentor.

“They said, ‘Well no, we haven't mentioned this to Johnny,’" says Letterman. "And I said, ‘Well, you know, I can't have this conversation until I know that it's okay with Johnny.' And that's the last I heard.”

"Oprah's Next Chapter" airs Sundays on OWN.