Lamar Odom’s condition is slowly improving but the former NBA star at times forgets his own name after his drug overdose, a source told ET Online Monday. Khloé Kardashian’s estranged husband has been receiving treatment at the Cedars-Sinai hospital in Los Angeles after he was found unconscious in a Las Vegas brothel in October.

"He's not doing great," the source, close to Odom, told ET Online. "His speech is still slurred and he can barely walk on his own yet. He forgets a lot of people's names -- sometimes even his own. He definitely has some memory loss."

Last month, Kardashian said during an interview with Ellen DeGeneres that Odom “has such a long way to go. He’s learning how to walk again and feed himself again and put sentences together, and cognitively there’s a lot. It’s a long, long road ahead.”

Kardashian, who called off her divorce with Odom after his hospitalization, has been by the 36-year-old’s side since his alleged drug overdose and has also been making all his medical decisions.

However, the reality TV star is not visiting Odom at the hospital as often as she used to during the first month after his hospitalization. Kardashian reportedly contracted staph infection at the same hospital where Odom is being cared for. However, the Kardashian-Jenner clan has been making constant visits, the insider told ET Online.

“They all pop in to see him [at Cedars-Sinai Medical Center], including Khloe,” the source reportedly said. Most recently, Kim Kardashian and her husband, Kanye West, took time out to meet Odom at the hospital on Thanksgiving Day and also made Odom listen to West’s songs from his seventh studio album, “Swish.”

"I'm thankful that Lamar liked my album," West reportedly said, while Kim said: “We did visit Lamar today, and we played him his new album… When it was done, I said, 'Did you like the music?' and he said, 'Loved it!’”

As Odom struggles to recover, it is unclear when he would be discharged from hospital. Last week, reports surfaced that he will be moved to a new rehabilitation facility closer to his estranged wife’s house in Calabasas, California.

Radar Online earlier reported that Kardashian, who is currently dating Houston Rockets player James Harden, had rejected Odom’s plans to move into her house after leaving the hospital.

“Lamar can’t stay at Cedars forever,” an insider told Radar Online. “He needs long-term care” and “his associates really would like for him to have a home health-care type of situation, but that may not be possible.

“Khloé has flat out refused to let Lamar move into her house,” the source told Radar Online. “She doesn’t want her house to be a hospital. She has been very clear about that.” The source also reportedly said that there are no plans for Odom to move in with his children, who live on the East Coast. “Lamar’s people want him to be in a quality care facility. But they are having trouble finding one that is secure and will provide him with the treatment he needs,” the source reportedly explained.