The 52-year-old "Batman Forever" star is working on a big screen project about Twain and his relationship with Christian Science founder Eddy.
The actor is yet to secure financing for the film, but he has already set his sights on his leading lady, reported Showbizspy.
"There's a lot of very talented actresses. I just talked to Cate Blanchett about it again. I've talked to her several times. It's hard to talk seriously, because I don't have a budget yet; I'm not financed," Kilmer said.
"But I think Mrs Eddy was a genius, so you have to think of genius actresses. Which is an interesting list, but a short list. There aren't that many geniuses, right? I think Cate's got genius in her," he added.
