Governor Paterson had planned to announce his selection on Friday or Saturday, but it was not clear how Ms. Kennedy’s move may affect the timing. The governor has been coy, and while he has praised Ms. Kennedy, he has also spoken approvingly of other candidates, including Mr. Cuomo and Representative Kirsten E. Gillibrand, who is beginning her second term in Congress from the Albany area.

Mrs. Clinton resigned from the Senate on Wednesday, immediately after being sworn in as secretary of state. The governor has said privately and publicly that he would like to select a woman to succeed her, noting that if he were to choose a man, the number of female senators would drop to just 16.

Some have speculated that with the state facing a $15 billion budget deficit, it would be risky for Mr. Paterson to bypass Ms. Kennedy, given her connections to the Obama administration and top Senate Democrats like Majority Leader Harry Reid. Mr. Paterson appeared to like Ms. Kennedy and saw in her a potential star, but was frustrated and angry by what he saw as efforts by her supporters, especially within Mayor Bloomberg’s administration, to create a sense of inevitability about her candidacy.

“She has pluses and minuses,” Mr. Paterson said in a radio interview earlier this month, adding that Ms. Kennedy “has a tremendous relationship with the president and that’s certainly a plus. She does not have much legislative experience, which is a minus.”

Image Caroline Kennedy left the Gee Whiz diner after an interview in New York in December. Credit... Stephen Chernin/Associated Press

There have been conflicting signals in recent days and weeks about whether Mr. Paterson had settled on Ms. Kennedy for the job. Mr. Paterson said earlier this week that he had chosen someone, but some advisers, as recently as Wednesday, remained convinced that he not yet made up his mind.

A friend of the governor’s said on Wednesday afternoon that “I would be totally shocked” if Mr. Paterson did not pick Ms. Kennedy.