The inquiry relates to an incident on June 18, which saw the two jets divert to Mildura Airport in regional Victoria after being unable to land at Adelaide.
The Virgin flight was forced to land despite aborting an earlier landing attempt after declaring a low-fuel emergency.
The Herald Sun understands it had only 800kg of fuel left on board and Mildura Airport CEO Bill Burke said that the plane did not have enough fuel for a second go-around.
The pilot should have been able to see the ground at about 120m, but due to the fog was not able to get visual clearance until the plane was just 25m from the ground.
The Qantas plane also breached the standard minimum visual requirement in order to land at Mildura, and landed shortly before the Virgin flight.
It is not clear why it landed first, as the Virgin flight declared a low-fuel emergency, and the Qantas plane did not.
Qantas spokesman Luke Enright said: «As a Qantas aircraft landed at Mildura Airport on the same morning as the Virgin incident occurred we are assisting the ATSB with its investigation.
«Our aircraft landed without incident.»
The Herald Sun revealed last week that there were problems with the automatic weather station at Mildura at the time of the incident.
The pilots of both the Qantas and the Virgin flights were not told of fog problems before they diverted from Adelaide.
A preliminary report into the incident is anticipated by July 18, while the final report is expected within 12 months.