Television personality James Corden speaks on stage at the Hollywood Film Awards in Beverly Hills, California November 1, 2015. NEW YORK -- "Late Late Show" host James Corden says he has no interest in taking over for his lead-in on CBS, Stephen Colbert. Play Video Broadway's biggest stars join James Corden in Carpool Karaoke Colbert's "Late Show" brought in a new executive producer in April and has been running neck and neck with ABC's "Jimmy Kimmel Live" in the ratings behind NBC's Jimmy Fallon.