The shooting occurred after Dorner burglarized a home, tied up a couple and stole their car, the source said.
It was not immediately clear whether Dorner was in custody.
A second source said there was an active crime scene but did not have details.
Law enforcement officials were swarming the area.
U.S. Marshal’s officials said in court papers that Dorner could have fled to Mexico. In Tijuana, Dorner was listed as one of the most wanted fugitives. But LAPD Lt. Andy Neiman said that was only one of many locations authorities were considering.
Neiman said detectives were examining video that might show Dorner purchasing scuba gear at a Sport Chalet store in Torrance days before his alleged killing spree began.
Law enforcement sources told The Times that officials have confirmed the man in the video is Dorner. He spent $5 to $10 to fill up a scuba tank, the sources said. Investigators have also reviewed store receipts.
Officers have crisscrossed California pursuing tips about Dorner’s possible whereabouts and serving warrants at homes in Las Vegas and Point Loma.
More information will be posted here as it becomes available.