Odom was texting and "speaking sentences" from his hospital bed, the person told the Los Angeles Times.
A spokeswoman for Odom's aunt also said he was improving.
"He probably has no idea we were there, but just to be there and to see him -- hopefully he knows there's a lot of guys that love him and want to see him do better and want to see him get better," Griffin said before the Clippers' Saturday practice.
A spokeswoman for Sunrise Hospital & Medical Center could not be reached for comment Saturday.
Odom regained consciousness Friday.
He was found unconscious Tuesday afternoon at the Love Ranch Vegas brothel in Crystal, Nev., about 80 miles northwest of Las Vegas. He had taken cocaine, alcohol and 10 doses of an herbal sexual-enhancement drug during a four-day stay at the brothel, authorities said.
Reality TV star
Kardashian and her family members Kim Kardashian, Kendall Jenner and Kylie Jenner have released statements saying they will not be posting to social media during Odom's health crisis.
Alvina Alston, a spokeswoman for Odom's aunt, JaNean Mercer, told The Times on Saturday evening that his condition had improved and that Mercer had spent all day in the hospital room with him.
Officials have sent blood samples to be tested hoping to find out what drugs may have played a role in Odom's condition.
Staff writers Melissa Rohlin, Amy Kaufman, Mike Bresnahan, Christine Mai-Duc and Javier Panzar contributed to this report.
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