E! said Odom was communicating using hand signals. Earlier on Monday, a family statement said Odom was improving steadily.
"Each day Lamar is getting stronger and reaching significant milestones in his recovery," a statement from Odom's aunt JaNean Mercer said.
"We are committed to remaining by his side as a family for our champion, who we love immensely.
"There has been an outpouring of support from Odom's former NBA teammates and his estranged wife Khloe Kardashian has been at his side."
Odom won NBA titles with the Los Angeles Lakers in 2009 and 2010, and married Kardashian in 2009 during a splashy televised wedding.
His connection to the celebrity Kardashian clan widened his fame, and while she filed for divorce in 2013, the split has reportedly never been finalised.
- AP