I struggle with this since I also want to read something I enjoy and not make it a chore. I tried reading Moby Dick recently and was so disappointed. I wanted to read the original but the old English threw me off and I found it boring.
I guess if I had any advice to offer to someone wanting to achieve that (if it's an achievement) it'd be to try older popular literature (try King Solomon's Mines, it's amazing, then work your way to even older stuff) to get used to older English (nb not Old English, which is another thing entirely and you're not likely to encounter much of it in anything but an extremely deep reading of English lit) and to read short, relatively easy "literary" works that are more recent. Vonnegut's way at the easy end. Maybe try Fitzgerald's The Great Gatsby or his short stories? Salinger's Nine Stories? I'm not sure—at this point I have trouble judging what's approachable. I'd make a terrible teacher of literature.
Lots of things kinda work this way. Jazz and "classical" music usually take some work on the listener's part, to personally learn and develop, before they yield their greatest fruits. Most folks have trouble enjoying silent films, but there are some damn good ones out there. Just takes effort and time.