>>4 Smart man.
You should read Haruki Murakami. He's brilliant. I'd recommend "Hard-boiled Wonderland and the End of the World" as an entry point, especially because it's the most "anime-like" of his books. Yoshitoshi Abe cited it as a big influence on Haibane Renmei, which becomes very obvious as you read it.
Some of his books do indeed feel "like anime", but I think that's more because they're all by Japanese artists and tap into Japanese aesthetics and psychological backgrounds and artistic traditions etc.
The other books are Cyberpunk like some anime but I don't think that's what you mean. I'd recommend looking into some other Japanese authors as well after Murakami; Ryu Murakami (no relation) is particularly good. Banana Yoshimoto's Kitchen is worth reading, too.
Some classic authors include Kenzaburo Oe, Natsume Soseki and Yasunari Kawabata, but I don't find them particularly "anime-like" beyond their common Japanese heritage.