The seat became vacant when Hillary Rodham Clinton resigned to become secretary of state in the Obama administration.
Kennedy, the daughter of the late President John F. Kennedy, had been viewed as the front-runner until her abrupt decision to withdraw late Wednesday.
Gillibrand, 42, is a second-term lawmaker from upstate New York.
The officials who described the events did so on condition of anonymity, saying they were not authorized to discuss them.
They stressed that the appointment still could go elsewhere, including to New York Attorney General Andrew Cuomo.
In an irony, Gillibrand was an official in the Housing and Urban Development Department during the administration of former President Bill Clinton at the time Cuomo headed the agency.
Paterson's most recent public disclosure on the vacancy came in writing, when he issued a statement saying Kennedy's decision "was hers alone" and that he hadn't ruled out any candidate before she withdrew.
Like other events surrounding the vacancy, her withdrawal created a swirl of confusion.
She called the governor around midday Wednesday and told him she was having second thoughts about the job, according to one person close to Paterson, who said she later decided to remain in contention, only to announce her withdrawal in an e-mail.
Paterson's appointment will serve until 2010, when a special election will be held to fill the final two years of Clinton's term.
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