ALBANY — Even Gov. David Paterson can see it might not be so sweet picking Caroline Kennedy for the Senate seat expected to be vacated by Hillary Rodham Clinton.

The Democrat said Kennedy, who has never held elective office, clearly has her drawbacks, despite her star power and private sector experience.

“Caroline Kennedy obviously does have a tremendous relationship with (President-elect Barack Obama) that’s certainly a plus,” Paterson said Thursday. “She does not have much political, I mean, legislative experience, which is a minus.”

That’s the first time Paterson has said Kennedy’s lack of legislative experience hurts her in competition with the veteran office holders also seeking the job Clinton would leave to become secretary of state.

Paterson, who will make the appointment, said as many as 15 contenders are interested and he’s already spoken to or interviewed about 10.

Kennedy, however, offers other advantages. Among them are her name and contacts in Washington — including her uncle, Sen. Edward Kennedy — that could give her immediate clout, much like former first lady Clinton.

Kennedy, a 51-year-old author and lawyer who famously guarded her privacy until December, gave a critical early endorsement to Obama during his campaign. Now, Paterson is lobbying Obama hard for an economic stimulus package to help New York out of a historic fiscal crisis.

Others said to be interested in the appointment include New York Attorney General Andrew Cuomo, Nassau County Executive Tom Suozzi of Long Island, and Reps. Carolyn Maloney, Steve Israel, Jerrold Nadler, Kirsten Gillibrand and Brian Higgins.