Percy doesn't like her.
Well, at least not in the way everyone thinks he does. No, he's not as oblivious as people think he is- he hears the rumors. Kind of expected them, actually- how could he not, with Annabeth's purple-dyed hair and ripped everything and his neatly pressed clothes and expensive car? Just becoming friends seemed like an anomaly, but it happened. She was blindingly smart and funny and Percy was a goner the moment he laid his eyes on her.
But he doesn't like her. No. Of course not. He just blushes when she compliments him because he's naturally that shy (it's quite annoying, actually). He sits on his hands whenever he feels the need to touch her because he doesn't want to make her uncomfortable (he's naturally a pretty touchy-feely friend, and she seems like the type to deck him after any unexpected touches). He ducks his head whenever one of her taller, better looking guy friends come over because he's intimidated (by the toughness and the fact that they could snap his neck just by blinking, of course).
No, Percy doesn't like her.
(But he probably does.)