People close to Odom remain hopeful that he didn't suffer significant brain damage in the hours before he arrived at Sunrise Hospital and Medical Center.
Odom was rushed to the hospital Tuesday after being found unconscious at a brothel outside Las Vegas. On Wednesday, a Nevada sheriff said the person who called 911 said Odom had recently used cocaine and had taken sexual-performance enhancers.
Authorities are retracing Odom's $75,000 visit to the brothel.
Nye County law enforcement and brothel officials said Odom's incident was a rarity for the Love Ranch, in the rural community of Crystal, Nevada, and have summed it up as a possible drug-related medical episode.
"We're going to be looking at the entire situation, how he actually came to be where he is now," Nye County Sheriff Sharon Wehrly said at a Wednesday news conference.
Authorities took a blood sample from Odom to find out whether he overdosed on drugs or alcohol, but the results could take several weeks.
Love Ranch owner Dennis Hof is cooperating with authorities, said Richard Hunter, a brothel spokesman and one of the people who called 911.
Odom's estranged wife, Khloe Kardashian, rushed to his side Tuesday night at Sunrise Hospital. Since then, friends, teammates and loved ones have visited and posted messages on social media asking for prayers.
"Obviously he's very close to this organization, so I think everybody's thinking about Lamar," Los Angeles Lakers coach Byron Scott said Thursday after practice. "One of the first thoughts on my mind when I got here this morning was had anybody heard any differently on what's going on with him. I think throughout the day, we're all thinking about him and we're all wishing him the best. Just praying. Just praying for him."
Scott said Lakers star Kobe Bryant, who was a teammate of Odom's from 2004 to 2011 and won championships with him in 2009 and 2010, was taking it hard.
"He's handling it," Scott said of Bryant. "It's hard on him. He was very close to Lamar. Loves him like a brother. It's just a rough time for Kobe dealing with that. This is probably the first time that he's had a teammate that's going through something like this."
Bryant did not speak with reporters, but he sent out a tweet Thursday that included the hashtag "#justpray."
Odom's maternal aunt and godmother, JaNean Mercer, thanked the public for its support. Publicist Alvina Alston issued a statement Friday on behalf of Mercer. The statement said in part: "No words can express the overwhelming gratitude we feel for the outpouring of support from around the world."
Lakers forward Metta World Peace, a childhood friend and former teammate of Odom's, said the only thing that is important right now is Odom and his family.
"Hopefully he gets well," World Peace said. "Hopefully he pulls out of this thing and gets the support that he really needs. That's pretty much all I have to say. ... There's nothing I can say that's going to make sense right now. It's all about Lamar and his children. That's the only thing that's important."
ESPN's Ramona Shelburne and Baxter Holmes and The Associated Press contributed to this report.
Lamar Odom showing small signs of improvement
Ramona Shelburne reports the latest on Lamar Odom's condition.
Odom found with blood, white substance coming from nose
Nye County Sheriff Sharon Wehrly says a 911 caller reported that Lamar Odom had been doing cocaine and using sexual-performance enhancers before his collapse.
Odom unresponsive, hospitalized
ABC News correspondent Kayna Whitworth reacts to the news that former NBA star Lamar Odom was hospitalized Tuesday after he was found unconscious at a Nevada brothel.