The FBI inquiry was revealed last week by a Oregon TV station KATU and the Oregonian, and corroborated Sunday night in a report in the Wall Street Journal.
The Oregonian has noted that Oregon's state health department "was able to pass federal reviews despite making little progress in its first year of work after winning a $48 million federal grant in February 2011." The newspaper also reported that, "The state initially promised the federal government to build a functioning exchange by February 2013."
The state's Cover Oregon insurance marketplace—which has been awarded more than $300 million in federal funds—also is being eyed by the inspector general's office of the U.S. Health and Human Services Department, the Government Accountability Office and an oversight committee of the U.S. House of Representatives.
Read MoreObamacare enrollments approach 8.02 million
Cover Oregon is considered to be among the worst-performing Obamacare exchanges in the country. The exchange, whose lead contractor was Oracle, was unable to enroll a single person in on online session, and instead had to rely on various workarounds to sign up people for health insurance plans.
Cover Oregon's board voted late last month to turn over private Obamacare insurance plan enrollment responsibility to the federally run exchange HealthCare.gov.
Oregon was one of 14 states which, along with the District of Columbia, ran its own exchange to sell competitively priced health insurance plans to individuals to help them comply with the Obamacare mandate that nearly all Americans have some form of such insurance this year or pay a tax penalty.
—By CNBC's Dan Mangan.