Kennedy told the New York Daily News that if Gov. David Paterson taps her to succeed Hillary Clinton as the state's junior senator, she "wouldn't be beholden to anybody," including Mayor Michael Bloomberg.
"I'm really coming into this as somebody who isn't, you know, part of the system, who obviously, you know, stands for the values of, you know, the Democratic Party," Kennedy was quoted by the newspaper as saying.
The daughter of slain U.S. President John F. Kennedy, Caroline has three children -- Rose, 20, Tatiana, 18, and John, 15 -- and is a lawyer married to Edwin Schlossberg, a designer and artist.
Of her children, the New York Post quoted Kennedy as saying, "Obviously, they were supportive of me, and think this would be an incredible opportunity. We talked about whether their life was going to change, and whether our family life was going to change and, you know, what kinds of ways and what could we predict."