The Kennedys: A long tradition of holding high political office
Caroline Kennedy, the daughter of late President John F Kennedy, is putting her name forward for the US Senate.
She is seeking to take over as junior senator for New York from Hillary Clinton, who is set to be secretary of state in the Obama administration.
New York Governor David Paterson, who will choose Mrs Clinton's successor, said Ms Kennedy had expressed interest.
She was a key backer of Barack Obama as he defeated Mrs Clinton to secure the Democratic presidential nomination.
Caroline Kennedy, whose father was assassinated in 1963, has spent a lifetime staying out of the political limelight, says the BBC's Matthew Price in New York.
But with the Kennedys less of a family and more of a political dynasty, that may be about to change, our correspondent says.
Ms Kennedy's name has been suggested for several weeks as a possible replacement for Hillary Clinton.
Democratic Governor David Paterson said Ms Kennedy had expressed interest in the Senate seat.
"She'd like at some point to sit down and tell me what she thinks her qualifications are," Mr Paterson said, who has indicated he has not yet chosen a successor to Mrs Clinton.
Some critics have said Ms Kennedy is a socialite blessed with high-profile connections and the pulling power of the Kennedy name.
Democratic New York Congressman Gary Ackerman voiced doubt over her readiness for office.
"She has name recognition, but so does J-Lo," he said recently, referring to actress Jennifer Lopez.
Caroline Kennedy's family history is intertwined with that of the US
Republican Peter King, who had already voiced interest in the seat, said news of Caroline Kennedy's own interest made him more determined to run.
Members of the Clinton camp, who were furious when Ms Kennedy and her uncle, Senator Edward Kennedy, endorsed Mr Obama during the primaries, are also concerned that she may take over Mrs Clinton's seat, correspondents say.
The seat was once held by Ms Kennedy's uncle Robert F Kennedy, who was assassinated in 1968.
Senator Edward Kennedy has brain cancer, and his illness has raised the possibility that the Senate could be without a Kennedy for the first time in some 50 years, the New York Times reports.
Whoever Governor Paterson chooses, they will face a special election in 2010 for the remaining two years of what would have been Mrs Clinton's term, and another election in 2012 to secure a full six-year Senate term.