Lamar Odom continues to receive treatment after being hospitalized almost a month ago

By Aurelie Corinthios
Updated November 11, 2015 12:05 PM
Credit: AKM-GSI

The Kardashian family continues to spend time with Lamar Odom, who remains hospitalized almost a month after he was found unconscious at a Nevada brothel Oct. 13.

On Tuesday, Kim Kardashian West, 35, and Kourtney Kardashian, 36, were spotted paying a visit to the former NBA star, 36, at Cedars-Sinai Medical Center in Los Angeles. They were accompanied by close family friend Jonathan Cheban.

The famous family, in particular his estranged wife Khloé Kardashian, has been by Odom’s side for much of his hospitalization.

On Monday, Khloé gave an update on Odom’s health during a Los Angeles signing for her new book, Strong Looks Better Naked, telling Extra it’s “a long road for him.”

“He is alive on his own, and no machines are helping him, which is great, but he still has a lot of physical and cognitive therapy to go through,” said Khloé, 31.

She added that his next challenge is relearning to walk, and that the former basketball player will “probably leave the hospital” once he is able to walk on his own or with the help of a walker.

Though Khloé called off their nearly-finalized divorce, she previously told PEOPLE that doesn’t mean they are back together and it’s not even in their “brains thinking about … having a relationship right now.”

At the signing, Khloé maintained to Entertainment Tonight that Odom’s romantic life is not his priority right now: “Even if he was 100 percent better, he has a lot of other issues he has to deal with, I think, before taking on any relationship. He’s doing better everyday, for sure, which is a blessing, but it’s going to be a long road and he has to walk that road. It’s going to be a long time.”

For her part, Khloé is still going strong with her boyfriend James Harden. She was spotted hitting the town with the Houston Rockets shooting guard on Sunday, and she told E! News at the book signing that Harden, 26, “has been great.”

“He’s been really supportive. Really understanding,” she added.

A source told PEOPLE on Tuesday that Odom is curious about Harden and has been asking visitors about him.

The source added that Odom, who is “doing very well in therapy and pushing himself,” has also been receiving visits from Kris Jenner “about twice a week.” Still, the source said the momager “doesn’t believe Khloé will get back with him.”