WASHINGTON — Caroline Kennedy is interested in the Senate seat that would open once Hillary Rodham Clinton becomes secretary of state, according to a close relative who says the Kennedy clan is fully behind her rising to the office previously held by her Uncle Robert. "I know she's interested," Robert F. Kennedy Jr. told The Associated Press in a telephone interview Friday. Once Clinton is confirmed to President-elect Barack Obama's Cabinet, New York Gov. David Paterson will appoint someone to fill the seat for two years. Democrats said Caroline Ken nedy and Paterson have already spoken about the seat, and she is interested. Kennedy is the daughter of President John F. Kennedy and a niece of brothers Edward and Robert.