Lamar Odom will be released from hospital "in the next 10 days".
The basketball star is currently being treated at the Cedars-Sinai Medical Centre in Los Angeles following a four-day drug and drink binge at a Nevada brothel but it is claimed doctors are preparing to discharge him from the facility.
A source said: "Lamar will be released from the hospital in the next 10 days. It's uncertain if he will go to a facility to continue physical rehab, or do it as an outpatient."
However, the 35-year-old sportsman's estranged wife Khloé Kardashian has insisted she won't be letting him stay with her.
A source told RadarOnline.com: "Khloé told Lamar that after he was released from the hospital, he would need to go to rehab for substance abuse addiction. Lamar balked and said no way. Lamar is still insisting he doesn't have a drug problem. He is still in denial.
"Khloé has made it clear, Lamar won't be staying with her. He has a loft in downtown Los Angeles, and there are other options that can be explored."
Lamar is said to have been taken off dialysis in the last few days and is "getting stronger every day".