The network and Alan Berger, Couric’s agent at Creative Artists Agency in Los Angeles, began talks in early December, said the people, who insisted on anonymity because the discussions are private. Time Warner Inc.’s CNN also has expressed interest in Couric, 53, two people said.

Both sides recognize Couric’s salary must be reduced for her to remain at CBS, one of the people said. This season, the “CBS Evening News With Katie Couric” is averaging 5.73 million viewers a night, according to Nielsen Co. data, behind NBC and ABC, and down 24 percent from when she took over in 2006.

“Katie is enjoying herself at CBS and is proud of her award-winning show,” said Matthew Hiltzik, her spokesman. Gil Schwartz, a CBS spokesman, declined to comment.