CNN reports the logistical part of the inquiry has been completed and investigators have spoken with all physicians and pharmacies tied to Houston.
However, authorities say they're still reviewing additional medical information and waiting for a toxicology report. That should be completed by March 23.
Officials also want to talk to Houston's 19-year-old daughter, Bobbi Kristina Brown.
So far, sources tell CNN there is no evidence of anything criminal.
Meantime, Houston's will was filed on Wednesday in Atlanta, and it leaves everything to Bobbi Kristina.
Houston's money will be put in a trust, and Bobbi Kristina will get part of it when she turns 21. She will get more of the money at age 25, and then the balance at age 30.
Houston, 48, died Feb. 11 in a Beverly Hills hotel room. The cause of her death remains under investigation.
The Associated Press contributed to this report.