The decision came after a series of deeply personal and political conversations, in which Ms. Kennedy, whom friends describe as unflashy but determined, wrestled with whether to give up what has been a lifetime of avoiding the spotlight.

Ms. Kennedy will ask Gov. David A. Paterson of New York to consider her for the appointment, according to the person told of her decision. The governor was traveling to Utica today and could not immediately be reached for comment.

If appointed, Ms. Kennedy would fill the seat once held by her uncle, Robert F. Kennedy.

Ms. Kennedy has been making calls this morning to alert political figures to her interest.

Ms. Kennedy’s decision is likely to have a major impact on the governor’s considerations as he mulls who should succeed Mrs. Clinton. Already, some other Democrats have pointedly questioned her credentials for the job. United States Representative Gary Ackerman, a Queens Democrat, said last week that he did not know what Ms. Kennedy’s qualifications were, “except that she has name recognition — but so does J. Lo.”

Others, including Mayor Michael R. Bloomberg have praised her abilities.

Ms. Kennedy first telephoned the governor on Dec. 3 to inquire about the job, but Mr. Paterson described that conversation as “informational” and said it was clear that Ms. Kennedy had not decided whether she wanted to pursue the position.

But since then, she has begun reaching out to key political figures in New York, including Sheldon Silver, the speaker of the State Assembly, and Thomas P. DiNapoli, the state comptroller. She has also hired Knickerbocker SKD, a prominent political consulting firm headed by Josh Isay, a former chief of staff to Senator Charles E. Schumer, to advise her.

Ms. Kennedy’s family members, especially her cousin, Robert F. Kennedy Jr., have urged her to seek the post.

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