Sheen has recorded a video plea, sent to ABC News, asking the ex-Los Angeles police officer, who is suspected in three revenge killings and now the subject of a massive manhunt, to call him so they can talk things out.
"Mr. Dorner, this is Charlie Sheen," the actor said in the video. "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."
"Call me," Sheen added. "I look forward to talking to you."
Sheen was among the celebrities mentioned in Dorner's 6,000 word online "manifesto." Dorner wrote, "Charlie Sheen, you're effin awesome."
Over the weekend, Los Angeles police announced a $1 million reward for information leading to Dorner's arrest.
Recently, Sheen loaned Lindsay Lohan money, donated $75,000 to a fund for a 10-year-old girl fighting a rare cancer and offered his former "Two and a Half Men" co-star Angus T. Jones a spot on his new show, "Anger Management," after Jones bashed "Two and a Half Men."