Sources said that Odom said "good morning," gave the doctors a thumbs-up and he is breathing on his own.
The 35-year-old was rushed to the hospital Tuesday afternoon after employees at the Love Ranch brothel in Crystal, Nevada found him in his VIP suite and called 911.
His condition was also not clear and it was not clear how long his eyes were open for.
Dennis Hof, who owns the brothel, said Odom had been taking herbal Viagra and had drunk part of a bottle of cognac.
Two women at the ranch went to check on Odom and found him face down and unconscious.
"He was unconscious, but breathing. He had blood coming from his nose and his mouth along with a white substance," Nye County, Nevada Sheriff Sharon Wehrly said.
Odom's estranged wife Khloe Kardashian has been by his side at Sunrise Hospital in Las Vegas. She and some of her family - Kim, Kendall, Kylie and Kourtney - took to their websites Thursday night to release a statement about Odom.
"As a family we've decided to hold off on publishing content across our apps while we continue to support and pray for Lamar," the statement read. "Thank you for your kindness and understanding during this difficult time."
Meanwhile, Odom's aunt JaNean Mercer said, "No words can express the overwhelming gratitude we feel for the outpouring of support from around the world. Please continue to keep in your prayers, our family and Lamar, whom we deeply love, admire and cherish. His complete healing is paramount and our primary focus. Please respect our privacy as we continue to lean on GOD and trust in Him during this extremely difficult time."
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Odom last played in the NBA in 2013 with the Los Angeles Clippers. He spent the best years of his career with the Los Angeles Lakers, winning two championship rings and the NBA's Sixth Man of the Year award in 2011.
Odom emerged as one of the most promising basketball talents of his generation after a difficult childhood in Queens, where his mother died of cancer when he was 12 and his estranged father was addicted to heroin. Despite his accomplishments on the court, Odom's life never seemed free of struggle and tragedy, most tragically the death of his infant son in 2006.
Odom and Kardashian were married in 2009, but divorce papers were filed in late 2013, which were signed by both parties earlier this year.
The Associated Press and ABC News contributed to this report.