Bill Beaird, 80, wept as he described watching the Dec. 13 shooting, the Los Angeles Times reported.
Beaird said his youngest son, 51-year-old Brian Beaird, of Oceanside, called him to say he was being chased by police but insisted he had done nothing wrong.
The father said he told his son to pull over anyway.
"He said he was going to do it, but he didn't do it," Bill Beaird said.
After a nearly hour-long chase, the Corvette hit another car, seriously injuring the other motorist, then spun onto a downtown sidewalk.
Bill Beaird said he watched a report from a television helicopter as the Corvette's driver staggered out of the car, briefly raised his hands, was shot and fell to the ground.
"I thought it was my son, but I wasn't sure," Beaird said.
Brian Beaird was unarmed. Preliminary information indicated that three officers fired more than 20 shots at him, the Times said.
Police Chief Charlie Beck said Thursday that he was "very concerned" after reading a preliminary report the shooting. Beck said he placed the officers on leave until the investigation ends, when they may receive discipline or further training.
Bill Beaird said his son was discharged from the National Guard in 1988 after undergoing surgery for a brain tumor and needed regular medical care.
An attorney for the family, Dale Galipo, said Brian Beaird had developed paranoia after the surgery.
"He was simply afraid and paranoid of the police, even though he has never been convicted of any felonies," Galipo said. "And that paranoia of the police is one of the reasons why he didn't pull over."
A claim is a precursor to a lawsuit. If the city rejects or refuses to settle the claim, Galipo said the family would file a wrongful death lawsuit in federal court.
The city attorney's office said it had no immediate comment on the claim.
