Charlie Sheen urges 'California murderer' to turn himself in - video
Dorner is accused of killing three people in California in an apparent act of revenge for being fired from the LAPD in 2008 for making a false report of brutality against another officer.
The 33-year-old man preceded his alleged murder spree with listing his favourite celebrities in a manifesto, describing Sheen as "effin awesome".
Sheen has now recorded a video for TMZ, in which he offers to speak to Dorner personally if the killings stop.
"You mentioned me in your manifesto, so thank you for your kind words," the Anger Management star says in the short message.
He concluded: "I am urging you to call me. Let's figure out together how to end this thing."
Other celebrities named in Dorner's manifesto included Ellen DeGeneres and Curb Your Enthusiasm star Larry David.
The search for Dorner has become the largest manhunt in the history of Los Angeles.