Lance Corporal Ben Hyde, from Northallerton, was among those shot dead while manning a police station in the town of Al Majar Al Kabir, last June, as they helped train Iraqi police.
The Redcaps were surrounded by a mob of around 500 locals, many armed with rifles and rocket grenades.
Now Defence Secretary Geoff Hoon is reported to have written to the soldiers' families, saying that his ministry's investigation is likely to conclude that the deaths were not preventable and therefore were not the Army's fault.
One parent, Reg Keys, of Bala, North Wales, whose son Thomas died in the incident, has said he believes Mr Hoon is attempting to soften the blow for the families ahead of the official inquiry findings.
He said: "In doing so, he has insulted us and the memories of six brave men.
"The deaths of my son and his friends were entirely preventable. He should resign now."
The leaked news of the findings has come before the official release of the inquiry report, which is due in about two months.
Ben's father, John Hyde, 56, of Northallerton, was not available to comment on the latest reports.
Within days of the murders, allegations about poor equipment, broken radio signals and a lack of ammunition and back-up support for the six officers were widely reported.
A spokeswoman at the Ministry of Defence in London said today: "We do not comment on private correspondence involving Mr Hoon or anyone else."