Alexandra Datig claims Elder checked to see whether his gun was loaded during an argument about the couple's breakup at the time.
Datig also alleges Elder pushed her in 2014.
In a statement, the LAPD said it "was made aware of domestic violence accusations against Larry Elder, a talk show host and candidate for California Governor."
"The Department is conducting an investigation however due to the confidential nature of domestic violence investigations the Department can not provide any specific details or statements at this time as they could compromise the integrity of the investigation," the statement said.
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Elder's campaign has not commented on the report -- but last week Elder denied that the gun incident had occurred.
Elder is the leading Republican in most polls in California's upcoming recall election.
All registered California voters - more than 22 million people - received ballots in the mail and more than 1.5 million people have already voted, according to ballot tracking data from Political Data Inc. Voters are asked two questions: Should Newsom be recalled and, if so, who should replace him? There are 46 replacement candidates, though Republican Doug Ose dropped out after ballots were printed and endorsed state Assemblyman Kevin Kiley.
The Associated Press contributed to this report.