WASHINGTON – Caroline Kennedy — daughter of a slain president, niece of senators, and zealous guardian of her own privacy — is interested in the Senate seat once held by her uncle, her cousin says.

Robert F. Kennedy Jr. said he and the rest of the powerful Kennedy clan are urging Caroline to seek the New York governor's appointment to the Senate seat now held by Hillary Rodham Clinton — and added she is ready and seriously considering it.

"I know she's interested," Robert Kennedy, who himself was prominently mentioned for the seat, told The Associated Press in a telephone interview Friday. "She spent a lot of her life balancing public service with obligations to her family. Now her children are grown, and she is ready to move onto a bigger stage."

Once Clinton, in line to become secretary of state, is confirmed to President-elect Barack Obama's Cabinet, New York Gov. David Paterson will appoint someone to fill the seat for two years.

The Kennedy family's connections and history cannot force Paterson to choose Caroline, but the family's strong support could increase pressure on him to pick her over lesser-known contenders. For Caroline Kennedy, seeking the Senate seat would be a significant departure from the life she has lived until now, protecting her family's privacy — and her own.

Robert Kennedy said his extended family would come out en masse for her if she does get the appointment and has to run for election in 2010.

"If she runs, you will see more Kennedys than you have ever seen in your life," he said.

An environmental lawyer who took himself out of consideration for the Senate seat earlier this week, Robert Kennedy said he is one of "many, many people" urging her to seek it, partly because of her lifelong advocacy on education issues.

"She's probably one of the leading advocates in the nation on public education," he said. "She feels a lot of the issues she's worked on are in danger of being shunted aside because of the economic crisis."

Democrats said Caroline Kennedy and Paterson have already spoken about the Senate seat, and she is interested.

After two New York Democrats said Kennedy and Paterson were expected to meet privately to discuss the matter Saturday, the governor's spokesman said they do not have a meeting planned.

Kennedy is the daughter of President John F. Kennedy and a niece of brothers Edward and Robert. Robert Kennedy held the New York seat from 1965 until his assassination in 1968. Edward Kennedy has been a senator from Massachusetts since 1963 and still uses the old Senate desk that Caroline's father used as a senator from Massachusetts before he won the presidency in 1960.

As a prominent member of the Kennedy clan, Caroline Kennedy Schlossberg is the kind of high-profile, historic figure who could overshadow many other New York politicians hoping to be Paterson's choice.

The governor has said he is in no rush to make a decision, and Clinton is not giving up the seat before she is confirmed to the Cabinet post.

"The governor has not yet reached out to any potential candidates," said Paterson's spokesman, Errol Cockfield. "He has been approached by several candidates. Any discussions related to that selection are private, and the governor will not comment about speculation before a decision is made."

Whoever Paterson appoints would serve for two years and then have to run in a special election in 2010, along with Paterson and New York's senior senator, Charles Schumer. The candidate would then have to run again in 2012.