Wood, who was best known for her roles in "Miracle on 34th Street," "West Side Story," and "Rebel Without a Cause," was 43 when she died on Nov. 29, 1981. The actress was sailing off the coast of California's Catalina Island with her then-husband, Wagner, now 87, and her "Brainstorm" co-star Christopher Walken. Wood was discovered floating face down, although it's unclear exactly how she entered the water.
Homicide Bureau Lt. John Corina of the Los Angeles County Sheriff's Department told reporters Monday, "We want to talk with Robert Wagner."
"He's a person of interest because he was the last person with her before she went in the water," Corina added. "He was the last person with her, arguing, before everything went quiet."
Corina said Monday that Wagner was the one who alerted those on the boat that Wood had gone missing.
"She's missing and he sends them to go looking," Corina said. "It's not that big of a boat."
The lieutenant said that Wagner then told those on board that a dinghy, which had been tied to the boat before her disappearance, was “now gone.”
"It doesn't make sense," Corina added. "It doesn't add up."
Corina emphasized that right now the department is "not pressing charges on anyone. We're still just trying to figure out what happened."
The Los Angeles County Sheriff's Department told ABC News last week in a statement, "Wagner has always been a person of interest. This is not new; nothing new to add."
Wagner has always denied any involvement in Wood's death, according to The Associated Press.
ABC News reached out to Wagner Monday, but didn't immediately hear back.
The Los Angeles County Sheriff's Department reopened the investigation into Wood's death in fall 2011.
In a statement released last Thursday, the department said after their 2011 press conference, they received "more than 100 tips and we followed up on every single one."
From those tips, the department said they have witness statements for the first time ever, detailing a new sequence of events from that fateful night.
"A witness provided details about hearing yelling and crashing sounds coming from the couple’s stateroom," the statement from last week said. "Shortly afterward, separate witnesses identified a man and a woman arguing on the back of the boat. The witnesses believed that the voices belonged to Natalie Wood and Robert Wagner.
"As you may recall, Natalie Wood was later reported missing from the boat. The statements from these new witnesses differ from the original version of events as related by previous witnesses, including the individuals on the boat," the statement added.
"Do we have enough to make an arrest at this moment? No," the statement said.
In 2013, the Los Angeles coroner's office amended Wood's cause of death to "drowning and other undetermined factors," after a new investigation determined the actress had bruises on her body that "appeared fresh and could have occurred before she entered the water."
The cause of death was also changed from "accident" to "undetermined."
Wagner publicly supported the new investigation and has reportedly called Wood's death a tragic accident.
Walken told Playboy magazine in 1997 that only Wood knows what happened that night, as she was alone.
In his 2009 book, "Goodbye Natalie, Goodbye Splendour," the boat's captain, Dennis Davern, wrote that Wagner and Wood had an argument while having dinner on the boat in which Wagner broke a wine bottle on the table.
Davern later wrote that Wood left to go to her stateroom afterward, but he heard the two arguing in their room, making him turn up the volume on his radio. He wrote that he later looked outside and saw that Wagner and Wood had come out onto the deck, and appeared to be arguing.
Wood was on board the Splendour with Wagner, Christopher Walken, who was her co-star in the film “Brainstorm,” after having dinner at a restaurant on Catalina Island. Both accounts agree that there was an argument and Wagner broke a wine bottle on the table.
ABC News' Luchina Fisher, Marilyn Heck, Julie Sone and Alex Stone contributed to this report.