Does it mean anything if a girl walks very close to you, in your personal space?

There's this girl at my school who I like and wonder if she might like me back. Whenever we walk together, she walks very close to me, in my personal space. It's not an accident. I've noticed if I move farther away, she moves towards me. We've only been talking for a few weeks but she seems very comfortable around me. She seems to also like being around me and hanging out.

Though, if I hint about the possibility of us going out, she doesn't really respond to it. But she's the type of person who likes to move slow so I don't know what to think.