In a statement, Spain's national police force, the Guardia Civil, said rescuers had found remains.
Slater, 19, an apprentice bricklayer from Oswaldtwistle in Lancashire, went missing after attending a music festival on the island four weeks ago. He was last seen walking alone in the Rural de Teno national park, a rugged and remote area on the opposite side of the island to the holiday resort where he had been staying with friends.
The statement said: "Guardia Civil agents belonging to the mountain rescue and intervention group located this morning the lifeless body of a young man in the Masca area, belonging to the municipality of Buenavista del Norte."
It went on to suggest the person "could have died due to an accidental fall on the cliff and inaccessible area where [the body] had been found".
Spanish police said that for 29 days different units of the Guardia Civil had run a "constant search... to look for the young man every day in the area of Masca", and would await the results of an autopsy to confirm the cause of death.
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