Deyan Deyanov apparently drew a finger across his throat as he made the chilling threat in a store on the holiday island.
A security camera inside the shop is understood to have recorded him holding his hands three feet apart as he added: “I want a knife this big,” it was reported.
The 28-year-old Bulgarian is believed to have stormed from the mini-market in Los Cristianos after he was ordered to leave.
The shopkeeper, who gave his name as Carlos, told the newspaper: “He wandered around looking for something. He had a note which he showed me – it said, ‘I am God’.
“I asked him what he was looking for and he held his hands far apart and said ‘I’m looking for a knife this big’.
“I asked him why he wanted it and he said, ‘I’m going to kill somebody’. He drew a finger across his throat to show how he would do it.”
The shopkeeper said he had then ordered Deyanov out of the store.
But he said he had not believed the homeless Bulgarian’s alleged threat had been serious.
His comments emerged as detectives in Tenerife faced questions over the circumstances of the brutal attack in which grandmother-of-five Jennifer Mills-Westley was repeatedly stabbed.
It is thought Deyanov, who was arrested after he allegedly fled the Valdes shopping centre, had previously received psychiatric treatment.
Regional newspaper La Opinion reported he had been released from a local hospital in February after being involved in violent incidents. He holds a police record.
Since the attack on Friday morning, it has emerged that a terrified Ms Mills-Westley had sought refuge at a local employment centre just minutes before she was killed.
The tearful 60-year-old, originally from Norwich, Norfolk, is understood to have told social services officials in the building that she was being trailed.
The man was sent away and Ms Mills-Westley walked into a nearby Chinese-owned shop on Avenida Juan Carlos.
But moments later she was viciously stabbed and decapitated.
Witnesses said her killer left the store clutching her head and was reportedly saying “God is on earth”.
Her daughter Sarah paid tribute to her mother, saying: “She was full of life, generous of heart, would do anything for anyone”.
Ms Mills-Westley had been living in Tenerife after retiring from her job as a road safety officer with Norfolk County Council.