Kennedy's cousin, Robert F. Kennedy, Jr., said recently that she is interested in the Senate seat that would become open if Clinton is confirmed as President-elect Barack Obama's next secretary of state.
If that happens, New York Gov. David Paterson would appoint someone to the seat for a two-year period, after which they would have to run for election, and, if they won, run for re-election again in 2012.
The governor has weeks to decide, and Bloomberg said he wasn't going to try to insert himself into the governor's selection process.
"Caroline is very competent. The governor has obviously a lot of good candidates to pick from and I won't be presumptuous enough to try to insert myself into what's obviously a very difficult situation for him," the mayor said.
"Caroline Kennedy can do anything," he added, calling her hard-working, honest and as smart as anybody.
Kennedy has already spoken to Paterson about the Senate job.
Kennedy is easily the most famous contender for Clinton's seat, but there are plenty of others. New York Attorney General Andrew Cuomo is widely known in the state. Paterson could also pick Buffalo Mayor Byron Brown or Nassau County Executive Tom Suozzi.
There are also a number of House members in the running, including Reps. Carolyn Maloney, Kirsten Gillibrand, Steve Israel, Brian Higgins, Nydia Velazquez and Jerrold Nadler.
On Sunday, New York's senior senator Charles Schumer said he liked all the candidates and would not take sides before the governor announces his decision. Clinton has yet to weigh in on who she would like to see get her seat.
Kennedy has strong connections to incoming Obama administration officials - though Obama said he is not going to get involved in New York politics.
As a prominent booster of Obama's presidential bid, Kennedy spent much of 2008 taking bigger steps onto the public stage.
As famous as she is, she always has been viewed as almost painfully shy.
She met her husband, Edwin Schlossberg, while working at the Metropolitan Museum of Art. They married in 1986 and have three children.
She made a splash in early 2008 by writing an op-ed column for The New York Times declaring her support for Obama, saying he had the potential to be as inspirational to Americans as her father was in the 1960s. She also spoke at the Democratic National Convention.
She then hit the campaign trail with Obama and worked on the vice-presidential search that eventually settled on Joe Biden.
