Military police also want to interview three other members of the 2nd Battalion Parachute Regiment who have since left the unit, the Mail on Sunday reported.
The alleged killing is believed to have happened in southern Iraq when the eight paratroopers were patrolling in two vehicles.
The unidentified boy was alleged to have been attacked when the unit stopped several Iraqis in a car.
No comment from MOD
The Ministry of Defence in London refused to confirm or deny whether any parachute regiment soldiers had been questioned.
"Several investigations are ongoing and it would be inappropriate to confirm details," he said.
Members of the battalion were stationed around the southern city of Basra. It was not immediately clear whether the latest allegation was new or whether the boy's case was among others already being probed.
Last month, human rights group Amnesty International accused British soldiers of killing several civilians, and lawyers for 12 Iraqi families who say their relatives were unlawfully
killed have initiated a High Court action in London.