The Swedish actor played Perry Wright, the violent husband of Nicole Kidman's Celeste Wright, on the first season of the HBO programme, and garnered Golden Globe and Emmy Awards for his performance.
While it seemed that Perry met his end in the finale of the first season, Alexander has now indicated that he will appear in some capacity in upcoming episodes.
"I was on set, yes. I can't disclose what I did on set," he said coyly during an interview on "The Tonight Show Starring Jimmy Fallon" on Wednesday night, September 26, when asked about recent photographs which showed him on the TV set with his co-stars, including Meryl Streep, who has been cast as Perry's mother Mary Louise Wright.
"Maybe, I was acting. I might have been just moral support. I might have just made coffee for the ladies. I might have helped Meryl Streep with her acting... Not help, but just give her little pointers, fine tune it a bit."
During the chat, host Jimmy noted that Alexander must be thrilled to be working with Meryl, and the former "True Blood" star went on to explain that they had actually both been cast in 2014 sci-fi movie "The Giver", though never shared any scenes together - much to his disappointment.
"I did a movie years ago and one of the incentives was to work with Meryl Streep. It was a scene with Meryl Streep and I was very, very excited about it. I didn't sleep the night before. I was really excited about it. I showed up on set and I was like, 'Alright, where is Ms. Streep?'" the 42-year-old recalled. "And they were like, 'Oh no, she's in London. She's going to be a hologram in this scene because it's a sci-fi. So you're just going to stare into empty space here and say your lines and someone will read Meryl's lines off camera.' We didn't see each other. And she was still amazing - from London, I felt her presence."
Season two of "Big Little Lies" is set to premiere in 2019.