I look forward to hearing from you. (correct)
I look forward to hear from you. (wrong)
I look forward to hearing from you. (correct in formal writing)
I am looking forward to hearing from you. (correct in an informal context)
Simply we can use “I’m looking forward to your reply” in a personal letter or we can say non formal sense and “I look forward to your reply” in a business letter as a standard formulaic closing.