Britain's Foreign Office was investigating the claim by the militant Islamists since one of the missing workers was believed to be British, The Guardian said.
The British newspaper said the deaths were also reported by government officials in Greece and Italy.
The hostages were employed by a Lebanese company and were captured Feb. 16 in a restive area north of Bauchi.
A splinter group of the Boko Haram rebels claimed responsibility for the abductions.
A statement on an Islamist Web site said the hostages were killed after British military planes landed at a Nigerian airfield, The Guardian said. The statement claimed the planes were there to take part in a rescue raid; however, British officials have said the aircraft were on a routine mission.