Dorner, 33, posted the manifesto online last week after allegedly killing the daughter of a retired Los Angeles Police Department captain and her fiance. He also is alleged to have shot three police officers, one fatally, in Riverside County.
In his manifesto, Dorner said he was seeking revenge for his termination in 2009 for allegedly making a false accusation against his training officer. He threatened "unconventional and asymmetrical warfare" against police officers involved in his dismissal and their families.
He also expressed his admiration for Sheen, Michelle Obama and Anthony Bordain, the Los Angeles Times reported Sunday.
"Charlie Sheen, you're effin awesome," Dorner wrote.
Sheen issued a plea to Dorner in a short video posted on TMZ Saturday.
"You mentioned me in your manifesto, so thank you for your kind words," Sheen says.
"I am urging you to call me. Let's figure out together how to end this thing. Call me. I look forward to talking to you."
A massive manhunt for Dorner has focused on the Big Bear mountains since Thursday, when his pickup was found in flames on a forest road between Bear Mountain and Snow Summit ski resorts.