The insider also claimed he has been taken off a ventilator and is breathing by himself.
Another source confirmed he is speaking and functioning, and that his family, including his children, Destiny, 17 and Lamar Jr, 13, with ex-girlfriend Liza Morales, are all by his side at Sunrise Hospital in Las Vegas.
Alvina Alston, a spokesperson for Odom's aunt, JaNean Mercer, told Entertainment Tonight he said, "Good morning" to his doctors and when asked if he wanted to see his children, he replied: "Yes".
But an insider told gossip website TMZ.com that doctors believe it's still too early to tell whether Lamar will be able to sustain breathing on his own, so they plan to go back and forth between a mask and a ventilator before officially deciding to take him off life support.
The good news comes just hours after test results showed Lamar's heart function is "much better."
The athlete was allegedly found with "virtually every drug imaginable" in his body and suffered multiple strokes.
- Bang! Showbiz