Barnett also helped put together television deals for Brian Williams, Lesley Stahl, Neil Cavuto, Christiane Amanpour, Dr. Sanjay Gupta and others.
Barnett declined to comment on the story.
Palin, John McCain's polarizing running mate, is seen as one of the leading contenders for the GOP presidential nomination in 2012. She would likely garner a significant advance for a book on her life and rise to national prominence.
Television producers would also be interested in retaining Palin, a former sports reporter who would likely have an easy time transitioning to a television role.
Former Arkansas Gov. Mike Huckabee, who became nationally known during his run for the 2008 Republican presidential nomination, began hosting a show on Fox News in September.