The governor plans to announce his choice at a news conference Friday.
Caroline Kennedy appeared to be the front-runner for the seat until she unexpectedly withdrew from consideration Thursday.
The Albany Times-Union reported that a highly placed source said Gillibrand was the choice, telling the newspaper Paterson had called members of the New York congressional delegation to let them know. The Times-Union said another source, also highly placed, reported that Paterson had called at least one of her rivals, also to say he had picked Gillibrand.
Kennedy, daughter of the late President John F. Kennedy, said she was bowing out for personal reasons, but sources told The New York Times problems involving taxes and a household employee surfaced during the vetting process.
A Kennedy aide, while not denying issues emerged during the vetting, told the Times nothing surfaced that would have disqualified her.
During the Clinton administration, Gillibrand was on the staff of Housing and Urban Development Secretary Andrew Cuomo, who was also a contender for Clinton's seat. In 2006, Gillibrand ousted Rep. John Sweeney, R-N.Y., from the upstate district he had represented for four terms.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Boston schools pull out free condoms over wrapping complaints