Odom had been recovering at Sunrise Hospital since last Tuesday after he was found unconscious at the Love Ranch brothel in Crystal, Nevada. Previously the transfer was contingent upon whether Odom's condition was stable enough to make the trek.
The ability to make the trip would be a good sign for Odom, who has been making strides since his hospitalization. Still, a source close to the family told ET on Monday that Odom is "still very weak." He continues to receive dialysis after kidney failure.
"He is showing improvement in his condition, however, regaining complete organ function continues to be a top medical priority," the source said.
A spokesperson for Odom's aunt, JaNean Mercer, previously told ET that the NBA star had opened his eyes and was able to communicate on Friday, after being placed in a medically induced coma on Wednesday. When his doctor asked how he was doing, Lamar gave a thumbs up and responded, "Good morning."
Odom would be heading back to familiar territory as he continues his recovery. The former pro basketball player played for the Los Angeles Clippers and Los Angeles Lakers at different points in his basketball career, winning two championships with the latter in 2009 and 2010. He was also named the Sixth Man of the Year as a Laker in 2011.
His relocation will also make visits easier for his ex, Khloe Kardashian, and the rest of the Jenner-Kardashian family, who have been by his side throughout his hospitalization.