Could we be friends?

So, there's this new girl at my job who I know somewhat from school (college). She's cool, and every since she started working at my job we've conversated a couple of times and I actually enjoy our conversations. The thing is that I'm not really a ppl's person and more on the private side. Also, at school she hangs around ppl who I don't care much for and would never hang out with them if someone paid me. They keep up drama and always have mess going on and I'm not into that. In most cases ppl tend to hang with those they have more in common with and being that her friends are not my cup of tea I am kinda sketchy about associating with her. Could we be friends since we both enjoy conversating at work ? Or should I just be friendly and at the same time keep her at a distance? Any thoughts?