The actor, who battled addictions to drugs and alcohol for decades, slipped into a coma a week ago in Los Angeles.
"He seemed fine early last week," his manager Phil Brock told People.com Thursday. "He had spoken with his agent and his management team and even attended an autograph signing. He really seemed in fine spirits."
Brock said he remains hopeful Conaway will recover.
"We hope he can finally exorcise the demons that have plagued him. He is an amazingly kind soul and there are many people who care about him," Brock said.
"Over the weekend, there was head movement, but there have not been any changes in his movement or condition since then. We are concerned it may have been an overdose but we have no way of knowing for sure."