"This is the most positive stuff we've had since it happened," a source close to Odom tells PEOPLE
Credit: Jason LaVeris/FilmMagic

Lamar Odom‘s loved ones are more hopeful than they’ve been since the former NBA star was rushed to the hospital Tuesday.

Odom woke up for the first time Friday after being in a coma for four days, and a source tells PEOPLE it has given his friends and family hope.

“This is the most positive stuff we’ve had since it happened,” a source close to Odom tells PEOPLE. “We’ve been on pins and needles. We’ve got a little bit of hope now.”

The source says that Odom’s condition is improving.

“The CAT scan came back clean, and they’re slowing taking him off each machine,” says the source. “He’s off dialysis and that looks good. We’re hopeful.”

Odom’s estranged wife Khloé Kardashian has been by his bedside in Las Vegas and was able to get a response from him when she bent down and told Odom, “I love you,” says the source.

“He nodded, and that was the first response we got from him. That was so encouraging,” says the source.

Odom was admitted to the hospital Tuesday after being discovered unconscious in a Nevada brothel. He had cocaine and opiates in his system, a source confirmed to PEOPLE. The source also confirmed he had suffered multiple strokes.

Earlier Friday, Odom’s former youth basketball coach and mentor Gary Charles expressed his joy over the positive development of Odom waking up.

“Once he gets out of this tough situation, he will have learned that there’s a whole lot of people rooting for him and letting him know they love him,” Charles told PEOPLE.