ALBANY, N.Y (AP) — Caroline Kennedy told New York’s governor on Monday that she’s interested in the U.S. Senate seat being vacated by Hillary Rodham Clinton, making her the highest-profile candidate to express a desire for the job.

Democratic Gov. David Paterson will choose the replacement.

“She told me she was interested in the position,” Paterson said. “It’s not a campaign. She’d like at some point to sit down.”

Caroline Kennedy’s spokesman, Stefan Friedman, declined to comment.

Clinton is expected to be confirmed as President-elect Barack Obama’s secretary of state.

At an afternoon news conference to discuss last week’s paralyzing ice storm, New York’s senior senator, Charles Schumer, said he has also talked to Caroline Kennedy about the job.

“And she’s clearly interested,” he said.

Kennedy is the daughter of the late President John F. Kennedy. Her uncle, the late Robert F. Kennedy, once held the Senate seat she wants. Paterson has sole authority to name a replacement for Clinton, who was first elected in 2000 and re-elected by a wide margin in 2006.

Over the past week, Kennedy, who lives in Manhattan, has reached out to several prominent New York Democrats to tell them of her interest in the Senate seat. They included Joel Klein, chancellor of the New York City Department of Education. Kennedy worked closely with Klein as executive of the Office of Strategic Partnerships for the New York City Department of Education, where she raised about $65 million for the city’s schools.

“I think she’s thought about it a long time,” Klein said of a conversation he had with Kennedy on Monday. He said the campaigning she did for Obama this year helped acquaint her with the gritty rituals of retail politics.

“She’s a highly determined woman and she’s clearly been thinking about her life and how to make an effective contribution,” Klein said. “Everyone knows Caroline, and everyone has a great historical respect for the Kennedy family.”

Other Democrats who appear to be on Paterson’s short list include New York Attorney General Andrew Cuomo, who won’t say publicly whether he’s interested.

One of the early front-runners, Rep. Nydia Velazquez of Brooklyn, took herself out of the running Friday.

Paterson will appoint someone to fill Clinton’s seat for two years if she is confirmed as secretary of state.

Republicans wasted no time in criticizing Kennedy as unqualified for the job and unfamiliar with the state.

“If anything, it makes me more determined to run,” said Rep. Peter King, a Long Island Republican who has already expressed his interest in the seat.

“As far as record of achievement, I strongly believe that I’m much more qualified, much more experienced, and have an independent record,” King said. “Nothing against Caroline Kennedy, but I don’t think anyone has a right to a seat.”

The Rev. Al Sharpton, a prominent civil rights activist, said Kennedy called him Monday. For Democrats, Sharpton could be an important ally, and an early call on such political matters can be a critical show of respect. If Sharpton eventually supports Kennedy, his endorsement could go a long way in helping ease any criticism that a black candidate was passed over.

Sharpton said he disagrees with those who say she isn’t qualified to be U.S. senator.