Los Angeles Police Department detectives are in search of Edward Garcia Jr., 36, and his wife, Melissa Hope Garcia, 25.
Detectives and White's family said he met the Garcias near his Hollywood home, probably at an ATM.
A hotel employee found body parts in a backpack and wrapped in a blanket.
Police said they've recovered a knife used in the crime.
A security guard heard some noise coming from the Garcias' room. He asked them to quiet down a couple of days before White's body was found.
Detectives said they believe the Garcias convinced White to meet them at the hotel on the day after Thanksgiving.
The intent may have been to rob White, police said.
"That's what we're looking at," said Det. Richard Arciniega of the LAPD. "That seems to be where we're going with it. But again, until we talk to them, we don't know."
While the LAPD continues to investigate what happened in skid row, the Garcias are suspected of doing something similar 3,000 miles away in Pennsylvania, where they allegedly lured a drug dealer to a home to rip him off.
It happened in York, a town about 100 miles west of Philadelphia.
According to police there, a friend of the man the Garcias allegedly lured to their home shot at them when he spotted the couple. No one was hurt.
How and why the Garcias ended up in Los Angeles is still a mystery, as is their whereabouts.
According to White's family, he's been sober for 15 years and regularly helped other recovering alcoholics stay sober.
"Please help us find who did this to my beautiful son," said White's mother, Elizabeth Peterson.
Anyone with information on the Garcias is urged to contact the LAPD at (877) 527-3247.