O'Brien quipped on his last episode as "The Tonight Show" host last Friday that he would love to be portrayed by the Oscar-winning "Michael Clayton" and "The Chronicles of Narnia: The Lion, the Witch and the Wardrobe" actress if HBO decides to make a movie about how he was ousted from NBC.
"I've heard about Conan!" Swinton told Movieline.com at the Sundance film festival in Utah when asked if she'd consider playing O'Brien. "I'm so thrilled. ... I would just be only too happy. ... Yes, yes, yes, absolutely."
Ever the good sport, Swinton went on to propose switching places with the momentarily unemployed O'Brien for a while.
"What I really would love to do is get him to do some of the things I get to do. It would be nice if he were here at Sundance maybe, wearing this coat, talking about (my film) 'I Am Love.' ... Every girl should have a doppleganger," the actress told Movieline.com.
Notable deaths of 2014 [PHOTOS]