A British ministry of defence spokesman said he could not confirm the accuracy of the report in The Sun newspaper.
But he said there would be a briefing on Thursday on the findings of the investigation into the crash near Baghdad on January 30.
At least one round, probably from a Soviet-made Dshke heavy calibre machine gun, penetrated the fuel tank in the plane's right wing during the incident, according to investigators quoted by The Sun.
The "very lucky shot" caused a massive explosion that sent the C130
Hercules plummeting to the ground in a fireball, it said.
The plane was "hedge hopping," which means flying fast and low in a combat zone, usually a highly effective means of avoiding enemy ground fire, the newspaper said.
The downed aircraft was on a 70-kilometer trip north from Baghdad to the major coalition special forces base at Balad.
The Sun said it belonged to the elite 47 squadron, who move SAS and SBS forces covertly all over the world.
The defence ministry has declined to comment on reports that members of Britain's elite Special Air Service (SAS) were aboard the flight.
The crash was the worst single loss of life suffered by British forces inIraq since the invastion to oust Saddam Hussein in March 2003.
Arab and Islamist groups had claimed that a missile or rocket had shot down the aircraft, but the sources quoted by The Sun said the claims were false.