According to Broadcasting & Cable magazine, CBS wants to "land a superstar to take over" for Rather and the "Today" show diva is its top choice.
Couric has just 18 months to go on her $15-million a year contract with NBC, the weekly reports in its edition out today.
"Virtually everyone in the news pantheon who's younger than 60 is tied up even longer than Couric or simply doesn't want the gig," the magazine reports.
Rather has said he will retire in March.
CBS would likely name someone to take over the job on an interim basis — then make way for Katie when she becomes free in 2006.
Couric could command a salary of $20 million a year or more, the magazine reports.
Only David Letterman, who earns about $31 million a year from CBS, and Jay Leno, whose most recent deal pays him $27 million from NBC, would be paid more on network TV.
Couric's agent, Alan Berger, told the magazine "there's nothing to talk about" right now.
But reports that Katie could end up as the signature figure of CBS News are sure to send shock waves through the TV world.
CBS could kill two birds with one stone by stealing Couric. It would not only gain one of TV's few remaining superstar reporters, but would take her off the ratings-topping "Today" show.
That would probably be a bigger favor to ABC — where the Diane Sawyer-hosted "Good Morning America" is gaining on "Today" but still trails — than to CBS. It's wake-up show is in far third place.
Couric too might be open to a change of scenery — if not hours.
Katie has been getting up early for 14 years now.