The 35-year-old was flown by helicopter from the Sunrise Hospital and Medical Center in Las Vegas accompanied by his wife, reality television personality Khloe Kardashian, the celebrity news website E! News reported, citing unidentified sources.
Kardashian (31), who was in the midst of divorce proceedings with her husband at the time of his collapse, is nevertheless reported to have remained athis bedside since shortly after he was admitted to Sunrise Hospital on 13 October.
E! News did not identify the facility that Odom was being taken to or explain the reason for his transfer, but said doctors in Las Vegas had intended to move him if his condition remained stable.
Sunrise Hospital did not immediately respond to requests for comment.
Neither the Kardashian family nor Odom's representatives have given any official updates on his condition since he was found unresponsive at a legal brothel in rural Nevada called the Love Ranch.
Authorities and brothel staff said he had used cocaine during his four-day stay at the ranch and had taken as many as 10 tablets of a herbal sexual-enhancement supplement capable of dramatically lowering blood pressure and interacting with other medications.
The veteran forward of the National Basketball Association was reported on Friday to have emerged from a coma, opened his eyes and spoken briefly to Kardashian.
Celebrity media, citing sources close to the family or hospital, previously reported Odom had suffered a series of strokes and kidney failure, with doctors giving him a 50-50 chance of recovery. Despite signs of improvement, he is expected to face months of rehabilitation, according to reports.
His ordeal marked the latest twist in a stormy celebrity relationship that has played out in tabloid headlines and reality TV.
Odom and Kardashian split up in 2013 after a whirlwind romance and marriage chronicled on the TV show Keeping Up with the Kardashians and its spinoff series, Khloe & Lamar.
Despite his 14 years as an NBA player, including two championship seasons with the Los Angeles Lakers, Odom's relatively brief membership in reality TV's most famous family has been the focus of his media coverage in recent days.
