Korean is not English. You could have a degree in Korean Literature (or any other language) but if you don't have English classes, you don't have English classes. They don't care how well you write critically in another language. They mean English.
Our school has a class in French literature that has traditionally counted (and is filled with pre-meds trying to satisfy the requirement) but now apparently it no longer 'counts' for many schools.
If it's in the English department, then yes. I'll be taking Asian American Literature for one of my majors (English) next semester and it's offered through the English department.