Kennedy was in Syracuse starting an upstate tour as she begins her campaign for the appointment.
The daughter of the late President John F. Kennedy is the highest profile name among those interested in appointment to the seat, which was once held by her uncle, the late Robert F. Kennedy.
She met Wednesday morning with Syracuse Mayor Matt Driscoll and John F.X. Mannion, an upstate Democratic party power broker.
Her upstate outreach is similar to Clinton's "listening tour" in 1999 and 2000 when she first ran for the Senate.
Like Clinton, Kennedy faces criticism because she's never been elected to public office. Some also worry she would favor New York City interests over the rest of the state.
Gov. David Paterson will decide who gets the job. The new senator will have to run in 2010 to fill the last two years of Clinton's term and then run for a full term in 2012.
A Siena College poll released Wednesday found New York voters are divided over who should fill the seat and that approval ratings for Kennedy and Attorney General Andrew Cuomo are nearly identical.
More New Yorkers believe Paterson will choose Kennedy, by a 31-16 percent margin. Thirty-eight percent said they didn't know or refused to answer and 16 percent felt Paterson would pick someone else.
The telephone survey of 622 registered voters last week had a margin of error of about plus or minus 4 percentage points.