The felony charges stem from Hevesi's alleged use of state workers as personal aides and chauffeurs for his wife, a Democratic state official told the New York Times.
The official, who spoke on condition of anonymity, said that an impending deal with the Albany County district attorney's office will result in the resignation of Hevesi, a guilty plea, and an agreement that he will serve no jail time.
No deal has yet been reached, the official told the newspaper. Hevesi's lawyers are expected to meet with prosecutors to finalize a plea bargain.
The vacancy would need to be filled by a vote of the full Legislature, with Assembly Speaker Sheldon Silver and the Democrats having the power to select the next comptroller.