The movie was a hit with audiences and critics alike, with Basinger winning an Academy Award for her portrayal of Lynn Bracken, the prostitute who happens to look an awful lot like a big-name movie star.
If CBS gives the L.A. Confidential project a series order, comparisons to the movie will be inevitable.
L.A. Confidential also won the Oscar for Best Adapted Screenplay, and was nominated in another seven categories.
The 1997 film starred Guy Pearce, Kim Basinger, Russell Crowe, Kevin Spacey, James Cromwell, and Danny DeVito.