The three-car collision at about 6 p.m. PDT Aug. 24 was not reported to police, but a Times reporter said his car was involved. Adolfo Flores said his car was rear-ended by a vehicle that had been struck by Odom's Mercedes, the newspaper reported Friday.
Flores said when he tried to exchange insurance information with Odom, the former Los Angeles Lakers star asked why he needed it -- and said the damage "doesn't even look that bad."
The driver of the third car could not be reached for comment, the Times said.
Odom will lose his driver's license for a year after refusing to submit to chemical testing for drunken driving Friday, the California Highway Patrol said.
He was stopped on suspicion of driving under the influence after he was spotted driving erratically on the 101 Freeway in the San Fernando Valley just before 4 a.m. Friday.
Odom was unable to complete a field sobriety test. At a police station, he refused chemical tests to determine his level of alleged intoxication, Highway Patrol Officer Leland Tang said.
Under California law, drivers who refuse the chemical test have their licenses suspended for a year.
Odom, 33, was released Friday morning on $15,000 bond.
If convicted of DUI, Odom would be subject to a mandatory evaluation by the director of the NBA anti-drug program, the Times said, citing the league's collective bargaining agreement.
Odom was involved in a fatal crash in July 2011 when a motorcycle crashed into a livery cab in which he was riding in New York. The motorcycle spun out and struck a teenager riding a scooter, killing the teen, Awsaf Islam.
A free agent, he most recently played with the LA Clippers.
Yosemite climber falls 30 feet, suffers major injuries
Moore to attend retreat in to avoid Kutcher's wedding