The 74-year-old actor also opens up about the complex roles now available for actors in the later stages of their careers.
The pair played lovers over 30 years ago in the 1987 film, which earned Close her first Best Actress Oscar nomination. The 71-year-old actress has earned a total of seven Academy Award nominations throughout her career, and Douglas thinks it's about time she finally won.
"Well, Glenn, I think Glenn has been nominated seven times for an Oscar. She has not won!" Douglas told reporters at a Television Critics Association set visit to The Kominsky Method on Thursday, praising her Oscar-nominated performance this year in The Wife. "I think she's fabulous in The Wife. She's a dear friend."
"I mean, she's kicking a** this year, she can't stop," he continued. "So, all my support and help is with her."
Close has seen success in this season's awards circuit so far, taking home trophies for her role in The Wife at the Screen Actors Guild Awards, Critics' Choice Awards and Golden Globes, where she opened up in her acceptance speech about what it means to see success and meaningful parts at this stage of her career.
Douglas feels the same way about his role in The Kominsky Method, as he explained at Thursday's set visit.
"I think it's baby boomers, it's just the size of that audience that has led to the creation of these complex roles for older actors," he said. "It's been a deprived audience for a long time, having those kind of characters, and I think... there's a big audience out there."
"I'm a very old man, so when I get a script that says I'm going to be in a gurney for about four weeks, I'm happy," Douglas' co-star, Alan Arkin, joked. "No dialogue, I just have to stay here and look pained and have that thing up my nose -- I'm a happy guy! This guy's making me work, though. He's making me say the lines."
"[His career has taught me that] I've got a long ways to go," he expressed. "I never anticipated the kind of options that happened even as I reached the three-quarter of a century mark, and it's wonderful. It's exciting."
"This has been a real treat, too, because comedy is not necessarily something I've done a lot of, and the chance to work with somebody like Alan, that is so wonderfully gifted in his timing and his understanding of it and the great writing, is feeling like you've learned something new," he added.
As for what Kirk thinks of The Kominsky Method, Douglas said that his dad isn't the greatest fan of his performance -- despite it earning him a Golden Globe last month.
"I don't think he gets it," he cracked. "'You're not funny.' He doesn't think I'm funny. 'Alan's funny. But you're not funny.'"
The Kominsky Method season two will debut on Netflix later this year.