Dominic Elliott, 23, died Sunday at Scarborough General Hospital in East Yorkshire, The Daily Telegraph reported. He had been driven to the hospital from the artist's home in Bridlington by Hockney's partner, John Fitzherbert.
Police said Elliott's death was not a violent one, but may have involved something he ingested at a party Saturday night. Investigators were questioning the young man's family and friends, including Hockney.
"This is a sudden death and we will have to speak to people who worked and lived with the person who died, whether a world-famous artist or a next-door neighbor," a spokesman for Humberside Police said.
"I don't know whether he drank too much or someone slipped him something, but I suspect it may have had something to do with it," Walter Elliott, Dominic's grandfather, said. "David treated him more like a son than an employee. He even bought him a car."
Friends said Elliott, a native of Bridlington, went to work for Hockney after dropping out of the University of Yorkshire. Elliott and two other assistants served as chauffeurs and helped set up shows.
Hockney painted Elliott, a work titled simply "Dom."
One friend said Hockney was in "a state of shock" about the death.
Hockney grew up in Bradford, about 75 miles away from Bridlington. One of the first artists to be openly gay in his personal life and his work, he lived in Los Angeles for many years but set up a studio in Bridlington on the coast in 2005.