Should I say something?

My coworker and I have formed a work friendship. We talk freely about different things. She’s 17 and I’m 22. So we talk about different high school issues since they pertain to her. The issues include cliques, etc. Anyway, she’s mentioned she had a troubled home life. She has cuts on her arm and they are plain as day. I want to ask her if she needs someone to talk to outside of work because she has also mentioned she doesn’t have many friends. I dont want to overstep my boundaries or make things awkward. Should I just mind my own business and act like the cuts aren’t there?