The report said engineers have begun to address a small hydrogen leak in the engine section discovered during the Dec. 19 launch attempt.
The NROL-71 was originally scheduled to lift off on Dec. 7 from Vandenberg Air Force Base in California but was postponed to make way for an investigation into a problem with the holdfire system.
ULA has made three more attempts to launch the rocket since Dec. 8 but encountered technical and weather issues that prevented the company from sending Delta IV Heavy to space.
Iridium Communications CEO Matt Desch said in a tweet Thursday that the company expects the eighth batch of 10 Iridium NEXT satellites to take off on Jan. 7 aboard SpaceX's Falcon 9 rocket, according to the report.
Desch noted in a new tweet Monday that the company now expects the Iridium-8 mission to launch on Jan. 8 from Vandenberg AFB with Jan. 9 as the backup date.