The theft was discovered Monday at the Mediterranean-style villa in gated Mulholland Park. Law enforcement sources said there were no signs of forced entry and that many people had access to the house in recent weeks.
The Kardashians reported the theft, which included jewelry and other items.
The 8,000-square-foot home went into escrow 10 days after being put on the market last month for $5.499 million.
The couple moved out after Kardashian filed for divorce in December and resumed using her maiden name. Earlier that month Odom, the former Lakers and Clippers forward, was sentenced to three years' probation and three months of alcohol abuse treatment after pleading no contest to one count of driving under the influence.
Odom was arrested Aug. 30 after California Highway Patrol officers spotted him driving about 50 mph in his white Mercedes in a "serpentine manner" on the 101 Freeway. CHP officers said he continued past several freeway exits while authorities tried to pull him over.
Once stopped, he showed signs of intoxication and could not pass field sobriety tests, according to a CHP report.
Los Angeles police detectives were continuing their investigation into the reported home burglary Tuesday.