The Times said police were expected to present a case to prosecutors as early as Tuesday to determine if there was enough evidence to file charges over a theft of watches. It was not immediately clear who was a suspect.
A spokesman for "Mean Girls" actress Lohan declined comment.
The incident surfaced in the media last week when celebrity website TMZ.com reported that the troubled actress and her assistant were guests at a home in the Hollywood Hills, and the owner later reported a theft to the Los Angeles police.
The Los Angeles Times said the owner of the watches is not cooperating with their investigation.
If Lohan, 26, is found to be involved in a theft, it could pose serious consequences for the actress who was released from almost five years of formal probation in March this year.
She is still on informal probation until 2014 from a jewelry theft case last year, and officials could revoke her probation and send her back to jail.
Lohan, who rose to fame as a child star in "The Parent Trap" and other movies, saw her once-promising career derailed by a 2007 drunk driving and cocaine possession arrest.
She has been trying to clean up her tarnished image since being released from formal probation, with guest roles on TV sketch comedy show "Saturday Night Live," a cameo on "Glee" and filming the Lifetime television movie "Liz & Dick."
(Reporting by Piya Sinha-Roy; Editing by Bob Tourtellotte and Matthew Lewis)
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