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The shooting took place after 10 p.m. (0600 GMT) on Saturday night (January 21) around the location of a Chinese Lunar New Year celebration held in Monterey Park, the newspaper said.
It was not clear how many people had been injured or killed, or if the suspect was still at large.
Footage posted on social media showed injured people on stretchers being taken to ambulances by emergency staff. Around the scene of the shooting - reported to have been at a nightclub - police guarded cordoned-off streets, the video showed.
"Our hearts go out to those who lost loved ones tonight in our neighboring city, Monterey Park, where a mass shooting just occurred," Los Angeles City Controller Kenneth Mejia said in a tweet.
Tens of thousands of people had attended the festival earlier in the day.