Moore returned to Britain on New Year's Day after more than two years in captivity. The bodies of three of his four bodyguards had already been returned, but one, Alan McMenemy, is still missing.
A source close to Asaib Ahl al-Haq, or the Righteous League, told the Times McMenemy's body would not be handed over until the group's leader, Sheikh Qais al-Khazali, is free. Khazali, a hardline Shiite, has already been transferred from U.S. to Iraqi custody.
Moore, 36, and his four bodyguards were kidnapped in May 2007 at the Ministry of Finance in Baghdad, where Moore was working for a U.S. company. Experts believe the bodyguards were killed soon after their abduction.
The British Foreign Office has told McMenemy's family he is most likely dead. His father, Dennis, said Canon Andrew White, the Anglican vicar of Baghdad, told him there is at least a chance his son might be alive.