Lamar Odom is recovering at his Los Angeles home after receiving treatment at a Las Vegas hospital, a week after being found unresponsive at a Nevada motel.
The former NBA is making “miraculous” progress, even taking a few steps, according to a family statement.
Lamar Odom’s estranged wife Khloe Kardashian, his father and two of his children are with the former Lakers star.
Police are conducting tests to establish what happened.
Lamar Odom, who married Khloe Kardashian in 2009, has long struggled with addiction.
He won the NBA championship with the Lakers in 2009 and 2010 and was named NBA Sixth Man of the Year in 2011.
Lamar Odom last played in the NBA in 2013 with the Clippers.