Steven Cook, 20, from Sandbach, Cheshire, was last seen in 2005 outside a pub in Malia asking for directions.
According to reports, a human skeleton was found near the area of the last reported sighting, along with a disposable camera and belt.
Cheshire Constabulary said it was aware of the discovery and was liaising with Greek authorities.
The family of Mr Cook has also been informed, police added.
More about the find and other stories from across Cheshire
Det Insp Gary McIntyre said: "At this early stage, the remains have been removed and will be examined in Greece to determine whether they belong to a female or a male."
Mr Cook's mother Pat told The Sun newspaper: "We have been told that a skeleton has been found - we don't know what to make of it. It was a shock to receive the call after all this time, it's upset all the family.
"But it's not the first time this sort of thing has happened. We are waiting to hear more from the Greek authorities."
Human remains have been found on a Greek island where a British tourist went missing 12 years ago.