03/23/2011 03:46 pm ET | Updated May 25, 2011

Katie Couric To Letterman: 'I Could Leave' CBS (VIDEO)

Katie Couric had a rather awkward conversation with David Letterman about her future with CBS on Tuesday's 'Late Show.'

Couric's contract is up in June, and her future with the network remains unclear. There have been rumors that she could leave the "CBS Evening News" and start her own talk show, or remain in the anchor chair for a limited time, or do something else entirely. Letterman didn't ask for specifics, but he did tackle the issue directly.

"I understand that you're thinking of taking another job," he said. "I have no idea at this point," Couric replied. That wasn't good enough for Letterman, though.

"Theoretically, you could leave the network," he said. "Theoretically, yes, it means that I could leave," she said. Letterman asked whether she would, in fact, depart. "Well no, I mean, I'm figuring out what I want to do," Couric said. Letterman said that, in his view, "once you take the anchor chair, that's what you do."

"Really?" Couric said. "Is that a CBS law?"

"it's not a temp gig," Letterman replied. "Five years isn't too temporary," Couric said.