Al-Khazali's reported release will raise hopes that McMenemy will either be released or his body returned.
Ali al-Dabbagh, an Iraqi government spokesman, said earlier this week that he expected McMenemy would be handed to British authorities in Baghdad within the coming days, but did not specify whether the bodyguard was dead or alive.
Neither Iraqi nor British officials have publicly linked the release of Asaib Ahl al-Haq leaders to efforts to free or recover the bodies of the hostages, but Khazali's brother Laith was freed in June shortly before the bodies of two of the guards were handed to British authorities.
A spokesman for the Asaib Ahl al-Haq was reported as confirming Qais al-Khazali's release to the AFP news agency, but an Iraqi politician claimed his case was still being considered.
"He is still in jail and his file is in front of the Iraqi judiciary system ... he faces many arrest warrants and the judges must examine these charges," Sami al-Askari, a member of parliament's foreign affairs committee and a government liaison on the hostage issue, told Reuters news agency.
Al-Khazali was transferred into Iraqi custody last month after being held by the US military since 2007 for suspected involvement in the killing of five American soldiers.
Analysts suggested that the release of Asaib Ahl al-Haq leaders and the handover of Moore were part of an attempt to move the group away from armed activity before parliamentary election in Iraq later this year.
Britain's foreign office has denied any deal was done for Moore's release, saying the US transferred Khazaali into Iraqi custody under the terms of a bilateral agreement between Baghdad and Washington.