They've been working together for six months, but the truth is, he barely knows her. He knows some things: where she went to university and medical school, for example, and where she did her internship. He knows that she was arrested when she was seventeen, but she's refused to tell him why. He knows she doesn't believe in God, but she believes in people more than they deserve.
He knows silly little things like that she likes turkey sandwiches, no mayonnaise, for lunch, with the occasional salad or tuna sandwich to break up the monotony. He knows that even after all these years of subsisting on coffee, she still can't drink it without a packet of sugar. He knows that she keeps two toothbrushes (fresh ones still in their packaging) in her bag in anticipation of getting stuck at work overnight, one for herself and one for some less-prepared coworker (usually him; Foreman doesn't like to stay, and House never asks).
He knows that she never complains when it's her turn to watch over a patient all night. He knows that she never runs off at the end of the day to go on a date or meet friends. She's never mentioned a boyfriend, but he assumes she has friends; how could someone like her not? He doesn't want to presume too much by considering himself her friend, but he can't believe she has no one outside the hospital.
He knows there's a lot more to her than a pretty face and a hot body, but he doesn't know most of it. Even if he is her friend, which he's not so sure of, he's not her confidant; if she shares her secrets, it's not with him. Maybe House has rubbed off on them, or maybe they were already damaged to begin with, but they keep their issues to themselves. She might tell him her story if he asked, but he's not sure he'd like the answer. It's easier to think of her as innocent.
He knows that she's different from the girls he dates, and not just because of that air of innocence. He likes that about her, likes her, but she's already rejected him and he knows better than to push. He knows she has a thing for House, even if he doesn't understand it at all. He's not the best judge of such things, but he doesn't think House is very attractive, and it isn't as though their boss is nice to her (or any of them, or anyone at all). Besides, he doesn't understand how someone like her who worries so much about being respected and taken seriously and simply being noticed for more than her appearance can risk her reputation by trying to date her boss. He thinks she must really love him to risk so much just to give a relationship a try, but he tries not to think about that more than he has to.
He knows he has no chance with her, and probably never did. He's not the type to mope over a girl, even one like her, so he puts it out of his mind. But he thinks that maybe he still has a chance after all this time to be her friend. Maybe if he tries he'll finally be able to put these fragments together and get to know her.