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.
Meanwhile, an associate of Dorner was being tracked by investigators, according to court records that suggest Dorner may have received help as he eluded a massive law enforcement dragnet.
Dorner, 33, a former LAPD officer, has evaded authorities since Wednesday night when he was named as the suspect in the slaying of an Irvine couple, a crime that preceded a wave of violence.
A criminal complaint filed in federal court raises the possibility that Dorner may have been assisted by an associate identified as "J.Y."
The search turned to Big Bear last week after Dorner's burning truck was found on a local forest road.
At the search's height, more than 200 officers scoured the mountain, conducting cabin-by-cabin checks. It has since been scaled back: About 30 officers were involved Monday and the San Bernardino County Sheriff's Department said about the same number would be out again Tuesday.
Authorities also asked residents in the Big Bear area with security cameras at their homes to review any video recorded after midnight Feb. 7 to see if images of Dorner had been captured.
Dorner allegedly threatened "unconventional and asymmetrical warfare" against police in a lengthy manifesto that authorities say he posted on Facebook. The posting named dozens of potential targets, including police officers, whom Dorner allegedly threatened to attack, according to authorities.
The records state that the manifesto was discovered by authorities Wednesday, three days after the slaying of the two Irvine victims: Monica Quan, a Cal State Fullerton assistant basketball coach, and her fiance, Keith Lawrence, a USC public safety officer.
Quan was the daughter of a retired LAPD captain whom Dorner allegedly blamed in part for his firing from the force in 2009.
The federal documents also provide new details on Dorner's alleged attack against officers early Thursday in Riverside County.
The first shooting was in Corona after an eyewitness reported a person matching Dorner's description at a gas station, telling an LAPD officer "who was detailed to the area to protect one of the officials whom Dorner had threatened," according to the court records.
"When the officer drove by the gas station, the suspect exited his vehicle and fired an assault rifle at the officer, hitting the officer's vehicle," according to the court records.
The LAPD later said the officer received a grazing wound.
About 30 minutes later, Dorner opened fire on Riverside police officers "who were in the area searching for Dorner," the documents said. On that detail, the account conflicts with a statement provided to the media by Riverside police officials, who said the officers were stopped at a red light and were not looking for Dorner.
Riverside Officer Michael Crain, 34, a married father of two who served two tours in Kuwait as a rifleman in the Marines, was killed in the attack. His partner remains hospitalized, Police Chief Sergio Diaz said, and it was unclear if he would be able to return to active duty.
Dorner was charged Monday with one count of murder, with special-circumstance allegations in the killing of a peace officer and the discharge of a firearm from a vehicle, in connection with Crain's death. He faces three additional charges of attempted murder.
Riverside Dist. Atty. Paul Zellerbach said because of the special-circumstance allegations, Dorner could be eligible for the death penalty if convicted.
Scanner won't connect for me, damn it. I need something to listen to while I play Mr. Mom.
