The 21-year-old's sister, who has asked for help in finding him onFacebook, said he is believed to have accepted a free ride to the largest of the Phi Phi islands from a local Thai man on Friday night.
He had previously been staying at the Pak Up hostel in the mainland resort of Krabi with friends.
A few hours later, Jordan contacted his mother and claimed he was unable to see them ever again.
Emily Jacobs told Mail Online: "Saturday morning, my mum received a message via Facebook from my brother, which basically said he can never see us again, that he is sorry he can't see us one last time, that he loved us."
After giving her a phone number, his mother Debbie called her son who told her he was upset and that "the man wouldn't let him leave. That he was scared of him," Ms Jacobs said.
The phone is understood to have belonged to another tourist who told Mr Jacob's family that Jordan had approached him and asked him if he could borrow it.
Ms Jacobs told the website that she had been in contact with him for "90 seconds" on Facebook messenger on Monday when he told her: "I need to keep you all safe," before saying: "I've said too much. I can't talk. I love you."
His sister told the Phuket Gazette that Mr Jacobs has mentioned visiting a Buddhist temple
Jordan's family have been unable to make contact with their son since.
In one of her latest Facebook updates, Emily said: "Any information, no matter how small you think it is, could be huge. Any sightings or potential sightings. Any contact. Anything. We want to have him home safe."
Phi Phi Police Chief Jetsada Junphum told the Phuket Gazette: "We’ve been in touch with all local businesses, but have had no sign of him. We’re worried that he’s already left Phi Phi."
Jordan is bearded, has black hair, and sports distinctive tattoos on his arms and chest.
He is estimated to be between 5ft 5in and 5ft 6in tall.
A Foreign Office spokesman said: "We can confirm that a British national, Jordan Jacobs, was reported missing in Thailand on 12 December 2015. We are providing consular assistance to the family."