Kennedy, 55, was a top backer of US President Barack Obama during both of his presidential campaigns and served as the co-chair of his vice presidential search committee in 2008.
Caroline's name is being vetted for the post, CNN quoted a Democrat familiar with the discussions as saying.
She is the only surviving member of JFK's family and has largely shunned the limelight and scrutiny associated with her famous last name.
After receiving degrees at Harvard and Columbia, Caroline served in a variety of roles at New York non-profits, including the John F. Kennedy Library and the American Ballet Theatre.