The body was discovered in the sea opposite the lighthouse in the city of Puerto de la Cruz where Amy lived.
The 28-year-old whale trainer vanished outside the Molly Malone Irish bar in the town on Thursday, November 29.
Also known as Amy Louise Docherty, she left the bar at 12.20am with her German boyfriend Dennis Kissling but has not been seen since.
A police spokesman confirmed: "I can confirm a woman’s body has been found in the sea. It is too early to say at this stage whether it is that of the missing Brit or not."
The woman’s body has now been brought to shore.
A police helicopter spotted a body floating in the sea around 11am this morning close to the lighthouse at Puerto de la Cruz.
Minutes later a Red Cross lifeboat raced to the scene and the woman’s body was pulled onboard.
It returned to the harbour were police held blankets up to prevent holidaymakers and a crowd watching the recovery operation.
A local councillor said: "We are pretty certain it is the body of the missing British girl. The body was spotted in a location where we have been searching and at the moment we only have one missing woman. Formal identification will take place later and then we will she a clearer idea of death from an autopsy but we are working on the theory it was an accident."
In surreal scenes holidaymakers carried on drinking and swimming as a dark coloured private ambulance arrived to take away the body.
It comes as witnesses said that as Amy and her boyfriend later walked out of the bar, Amy turned left and Dennis turned right, going their separate ways.
Yesterday her mother Julie and sister Chloe were in Tenerife, waiting anxiously for news, as police and coastguard choppers scoured the coastline for her amid fears she may have fallen into the sea.
It comes as CCTV footage obtained by The Sun showed her last known movements before she disappeared. The video was shot at the just past midnight on Friday morning.
Amy, 28, joins other drinkers dancing in a circle to the Pogues song Fairytale Of New York.
Standing next to fellow marine wildlife trainer and boyfriend Dennis Kissling, Amy at one point even turns and blows a kiss to the camera as she enjoys a night out with colleagues.
Dressed in skinny black jeans and a green jumper, Amy is recognisable with her mass of curly hair, swinging her arms in time to the music, smiling and holding hands with Dennis.
Molly Malone bar owner Brendan Reid Spencer told The Sun: “She came in with six work colleagues around 11pm on Thursday night when we have live music.
“They were all having a good time singing and dancing but I wouldn’t say they were drunk. She was with her fella, a German lad called Dennis. The group all left in twos and she and Dennis were the last to leave. She turned off to the right and Dennis went to the left.”
Uni graduate Amy, from Grimsby, Lincs, works at Loro Parque sea world in Puerto de la Cruz. German-born Dennis also works there. They are thought to have got together earlier this year and were at the bar celebrating a pal’s birthday.
Friends and family have posted appeals on social media and last night Spanish cops were following up a lead from a woman in England who said she had “seen Amy on Snapchat”.
Overnight local reports claimed officers from the island’s National Police UDEV unit – which in English stands for the Specialised and Violent Crime Unit – were now leading the investigation into Amy’s mystery disappearance.
And Julie said this morning: "We would like to thank friends and family for their continued support whilst the search for Amy continues."
Urging people to consider sharing the missing appeal posters with her daughter’s photo on them, she added: "We are all heartbroken and finding it hard to come to terms with the fact she’s missing.
"We desperately urge anyone with any information to come forward. Please if you were in the area on the night of Thursday March 29 and saw anything unusual or have holiday photos from that night, please look through them and think back."
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