Missing person expert Charlie Hedges said although police in Tenerife can’t search “forever”, they should be examining all lines of inquiry.
Ex-detective Hedges warned Jay’s disappearance could risk becoming a cold case if is not constantly kept under review.
It comes as police on the island yesterday called off the search for Jay, almost two weeks after he vanished on June 17.
Some 30 cops, firefighters and rescuers all took to the mountains in Masca – along with a handful of volunteers – on Saturday.
The hunt, which centred around Jay’s last known location, failed to find any trace of the teen.
Authorities on the island then dramatically revealed less than 24 hours later that the on the ground search had been ditched.
Cops have insisted, however, any tip-offs or new information will still be probed as the case remains open.
Hedges, who worked for Thames Valley Police, told The Sun detectives in Tenerife should not be discounting any theories at this stage.
Asked whether police should be probing whether Jay has been kidnapped or murdered, he said: “They should be keeping their minds open and examining all lines of inquiries.
“Police seem to have put a fair amount of resources into it.
“There is a judgement for when it is the right time to call off the search
“I had been wondering for a few days whether we were approaching that point. There is only so much you can search.
“But it may be appropriate to go back and search some areas based on the information they’re seeking at the moment.”
Hedges said Jay’s disappearance could become a cold case if all lines of inquiry become exhausted.
Jay, from Oswaldtwistle, Lancashire, vanished after a night out at the NRG festival at Papagayo nightclub in Playa de las Americas.
He was last seen travelling with the two mystery men in the north of the island in the Rural de Teno park.
Jay made a final frantic phone call to pal Lucy Law to tell her he was stranded in the “middle of nowhere” at about 8.50am on June 17.
Panicked Jay, facing an 11-hour walk back to their hotel, told her he needed water and only had one per cent of battery left on his phone.
His other friend Brad Hargreaves revealed a second call in which Jay told him he had veered off the main path – leading to speculation he may have slid down rocks.
It comes as…
Brad said he could hear the missing teen slipping on rocks during a final video call.
Search crews failed to find any trace of the teen before halting the search on Sunday.
He added: “As time passes, the chances of finding what’s happened or finding Jay diminishes.
“And so that does increase the probability of that [turning into a cold case] happening.
“But one does hope there are still things to be inquired into that will take us towards a satisfactory conclusion”.
It comes as Jay’s desperate family consider again asking British police to help find the apprentice bricklayer.
The 19-year-old’s loved ones were left “blindsided” when detectives on the island halted the hunt less than two weeks after Jay vanished.
The decision to dramatically cut off the search is the “nightmare scenario” Jay’s family were “dreading”, a source close to them revealed.
His parents Debbie Duncan and Warren Slater and brother Zak feared this weekend would be make or break in the hunt for the apprentice bricklayer.
A source back in the UK, who has been in regular touch with the family, told The Sun: “Jay’s family knew the search would eventually wind down. They get that.
“But it was a nightmare scenario they didn’t want to think about. And it wasn’t something they thought wouldn’t happen immediately.
“So for the decision to be made after just two weeks has left them bewildered and bereft.”
The source said Jay’s family “aren’t convinced” cops have scoured everywhere possible for clues.
They have vowed to stay in Tenerife to continue the search themselves, which they fear has been hampered by vicious trolls.
Jay’s family may also implore British cops to get involved after Tenerife authorities rejected their help.
Police on the island had insisted they had the resources they needed for the hunt before issuing a cry for volunteers for Saturday’s final search.
The source added: “They’ve been trying to get in touch with groups in Tenerife and beyond who specialise in missing persons
“They may also try to appeal, again, to the British Police to help. They don’t understand why the police in Tenerife wouldn’t welcome the extra support and help which was being offered.
“What did they have to lose? If every stone had been left unturned Jay’s family would be able to accept this. But it doesn’t feel like that’s the case.”