The arrangement for Hillary Clinton's longtime aide was created by the department while Clinton was secretary of state, the report said Thursday.
Abedin did not disclose the arrangement on her financial report, which requires public officials to publicize any significant sources of income, The New York Times said.
An adviser to Clinton, Philippe Reines, said Abedin, as a special government employee, was not required to do so.
Abedin's husband, Anthony Weiner, appears to be preparing for a mayoral run in New York City.
Abedin began the State Department arrangement in June 2012 and worked for Teneo, a strategic consulting firm, which was founded by Doug Band, a former adviser to President Bill Clinton, the Times said.
She also served as a consultant to the William Jefferson Clinton Foundation.
The Times said officials in the State Department and Clinton representatives seemed sensitive about the arrangement and did not wish to speak on the record.
Melanie Sloane, executive director of CREW, an ethics watchdog group, described the situation as unusual.
"If she was being held out as a deputy chief of staff, it would be highly unusual for her to be a part-time employee or a consultant," she said.