Caroline Kennedy, the daughter of the slain president whose public persona rose during this election year, was eyeing Hillary Clinton's Senate seat, the New York Times reported Saturday.
Clinton has been nominated by president-elect Barack Obama as his secretary of state, and if approved by the Senate, she will have to vacate her New York Senate seat.
Kennedy, whose father John F Kennedy was killed by an assassin in 1963, was a major supporter of Obama and played a surprisingly public role in his election, dpa reported.
The 51-year-old lawyer has kept a low public profile through the many years since her father's death, and through the years her mother, Jacqueline, who died in 1994, suffered cancer.
But she is surrounded by the mythic aura of the popular and powerful Kennedy family, and her endorsement of Obama early on gave him a strong boost.
The Times quoted Caroline's cousin, Robert F Kennedy Junior, as saying he believed "that she is considering it."
"A lot of people the last couple of weeks have urged her to do it," he was quoted as saying.
The New York Governor David A Paterson, who would choose a replacement for Clinton until the next election, confirmed Friday that Kennedy had called him to discuss the position, the Times reported.