Khalaf Mufdhi were detained in Basra and accused of involvement in the deaths of two British soldiers, Staff Sgt Simon Cullingworth and Sapper Luke Allsopp.
An Iraqi court later decided there was insufficient evidence to try the men.
In 2010, the pair were awarded damages by the European Court of Human Rights (ECHR) for mental suffering.
Allegations that the men were mistreated by British soldiers are now being investigated by the UK's Iraq Historic Allegations Team (Ihat).
Ihat was set up in 2010 to look at allegations of abuse by the British military against Iraqis between 2003 and 2009.
In October, Prime Minister Theresa May said her government would take action over the "industrial scale" of claims lodged with Ihat using legal aid funding.
It is not known how many troops are being investigated over the treatment of Mr al-Saadoon and Mr Mufdhi.
The two men, now both in their 60s, were accused of murdering Staff Sgt Cullingworth and Pte Allsopp. An inquest found that the British soldiers were ambushed by Iraqi militiamen, taken to an Iraqi intelligence base and shot.
Mr al-Saadoon and Mr Mufdhi were formally charged in 2006 with murder and war crimes but the charges were later annulled by an Iraqi court on the grounds of insufficient evidence.
Media captionThe defence secretary explains how troops will be protected from "vexatious" legal claims
The pair were eventually awarded £36,000 in legal costs and £75,000 each in damages by the ECHR for suffering caused by years of living in fear of execution.
The criminal claims against British soldiers were brought forward by Public Interest Lawyers (PIL), which closed in August after it was told it would no longer receive legal aid funding.