The 33-year-old allegedly threw champagne over British TV presenter Donatella Panayiotou during a night out at Hollywood nightclub Lure, the Sunday Mirror reported.
A spokeswoman for the Los Angeles Police Department (LAPD) confirmed they had received a battery complaint against Cole.
She said: "A battery report has been assigned to detectives from the Hollywood division."
Police have 30 days to investigate the complaint, which they received on May 31, before deciding whether to press charges, the spokeswoman said.
Cole was with a group of friends including former team-mate Shaun Wright-Phillips when the alleged incident happened, the Sunday Mirror reported.
A spokesman for Chelsea said it was a "private matter" and declined to comment.
Cole, who has 107 England caps, announced he was retiring from international football last month after he was left out of Roy Hodgson's World Cup squad.
The left-back's contract with Chelsea is due to expire this summer.
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