Lt. John Corina, of the Los Angeles County Sheriff's Department's homicide bureau, said in a press conference Monday that the details Wagner has offered up on the fateful night "really don't add up to what we've found."
"He's a person of interest because he's the last person with her before she went in the water," said Corina. "This is a suspicious death investigation. We want to know what happened from the time of the argument to when she got into the water."
CNN's calls to a representative for Wagner were not immediately returned.
Corina added that Wagner is not obligated by law to speak with investigators, but said "we're closer to understanding what happened, I think."
Last week, authorities said they were investigating the "Rebel Without a Cause" star's death as "suspicious" after new witnesses came forward.
Wood drowned in November 1981 while boating off Catalina Island in Southern California with husband Robert Wagner and friend Christopher Walken. She was 43 at the time.
In his 2009 book, Wagner wrote that during his trip with Wood and Walken, he became jealous and argued with both of them.
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