"Police received a telephone call at 2:30 am from a witness reporting the fall of human remains at an intersection in Mushrefa neighbourhood" in the Red Sea city, spokesman Nawaf bin Naser al-Bouq said in a statement.
Initial indications were that the remains "fell from a plan's landing gear," said Bouq, adding that investigations were ongoing.
In a desperate attempt to cross borders, some people at poorly monitored airports climb inside the bays holding the landing gear of planes. Most of them freeze to death once the aircraft reach cruising altitude, but some survive.
The man's body was found by a maintenance worker in Riyadh who was inspecting the landing gear of the Saudi-owned Nas Air Airbus 320 after it touched down there.