German national Jurgen Kantner is reported to have been beheaded by Isis-linked insurgent group Abu Sayyaf after talks to pay a 30 million peso (£480,000) ransom to secure his release broke down.
The Philippines military has said it is trying to confirm reports that Kantner has been killed.
While the Philippines had said in the past that it would not pay any ransom, it said that it would not intervene if the victim's family or any other party wanted to pay for Kantner's release.
Major General Carlito Galvez Jr, the chief of the Western Mindanao Command, confirmed receiving reports about Kantner's beheading but said: "We need body of proof."
He added: "Until sufficient proof is obtained ... our assumption remains that the subject kidnapped victim is alive and well. Do not believe unvalidated information going around until proven otherwise."
A police report released on Sunday (26 February) afternoon said that Kanter, 70, a sailing enthusiast, was killed at around 3.30pm local time in the Buanza district in the Sulu province by the group's unit leader, Muammar Askali, alias Abu Rami, the Straits Times reports.
"Despite efforts exerted by groups and the security forces, I have received reports about the alleged beheading of a German kidnap victim in Sulu [on] Sunday afternoon," said Jesus Dureza, the government's peace adviser and chief hostage negotiator.
Kanter and his wife Sabine Merz were cruising along a dangerous area of the Philippines when they were abducted by Abu Sayyaf, who are well known for kidnapping and holding foreigners for ransom.
Merz was killed after she reportedly tried to fight back against the militants with a shotgun. The couple had been sailing for several years onboard their 53-foot vessel, the Rockall.
Their voyage was not without incident. In 2008, they were held for 52 days by Somalian pirates and were reportedly only freed after a six-figure ransom was paid.