(CNN) - Caroline Kennedy, the 51-year-old daughter of President John F. Kennedy, has made it clear to high-level Democrats, including New York Gov. David Paterson, that she wants to be the next senator from New York, a source close to Kennedy has told CNN's John King.
Two other sources confirm her interest in filling the seat now held by Secretary of State-designate Hillary Clinton. One source is a senior Democratic operative.
Kennedy's interest in the seat could mean the continuation of a family legacy in the Senate that began 56 years ago with the election of her father as the then-junior senator from Massachusetts.
Her uncle Ted has represented Massachusetts in the Senate since 1963. Her uncle Robert served as New York's junior senator from 1965 until he was assassinated in 1968.
"Remember, this (Clinton's) seat in the Senate was once held by Robert Kennedy," CNN Senior Political Analyst Bill Schneider said. "Her other uncle, Ted Kennedy, is ill right now. If Paterson appoints Caroline Kennedy to the Senate, it means there could be a Kennedy staying in the Senate for quite a long time."
Before this year, Kennedy generally limited her forays into the public sphere to non-partisan activity, penning books on civil liberties and serving as the de facto guardian of her father's legacy.
But in January, she backed a political candidate for the first time, announcing her endorsement of Obama during the Democratic primary season with an op-ed in the New York Times that drew days of the kind of media attention she has spent her life avoiding.
"I have never had a president who inspired me the way people tell me that my father inspired them," she wrote. "But for the first time, I believe I have found the man who could be that president - not just for me, but for a new generation of Americans."
"Apparently she has acquired a taste for politics," Schneider noted. "She wants to be part of this new regime in America, clearly playing a key role in the Senate if she gets that appointment."
- CNN's John King and Kate Bolduan, and Mark Preston contributed
to this report.