Police said they suspected the missing teenager may have died after "suffering an accident or fall", but a post-mortem would provide details.
It is thought specialists on the ground in Tenerife found Jay's possessions and clothes.
His family were heartbroken after the body was discovered close to where his mobile phone was last active a month ago.
The apprentice bricklayer, 19, of Oswaldtwistle, Lancs, vanished on June 17, prompting a massive search operation.
Tenerife police announced they had called off the official search after 13 days, but yesterday revealed they had been continuing to look for him and that they had discovered a body.
While a formal identification has not yet taken place, officers said that "everything is pointing to it being" Jay.
The teenager's teenager's friend Brad Hargreaves, who flew to Tenerife with him and another friend, Lucy Law, posted a poignant tribute on Instagram, showing a picture of the two of them with a string of broken hearts and a crying emoji.
He said: "No words. Nothing will be the same without you. Rest easy, brother. Love you always."
A helicopter, believed to belong to a regional government emergency and rescue group, was used to recover the body using a winch because the terrain at the spot was too steep. Specialists on the ground are understood to have found possessions and clothes belonging to the teenager.
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