In a short video, the Anger Management star urged Dorner to contact him, saying, "You mentioned me in your manifesto, so thank you for your kind words. I am urging you to call me."
"Let's figure out together how to end this thing," Sheen continued. "Call me. I look forward to talking to you."
The former Los Angeles Police Department officer became the target of a major manhunt in California after he allegedly killed three people and injured two others, leaving behind a statement posted to Facebook.
"Charlie Sheen, you're effin' awesome," Dorner wrote in the lengthy read, paying tribute to the actor and many other celebrities including Ellen DeGeneres, Serena Williams, Natalie Portman, Kevin Hart and Jon Stewart.
A source told E! News Sheen decided to make the video "on his own," saying it wasn't "sanctioned by police," and that the thesp simply wants the killing spree to end.
Sheen's rep had no comment.
—Reporting by Ken Baker