Before Zelda is kidnapped, she says there is "something important she wants to tell [Link]". Gee, they're on a frickin' date and have been friends since they were kids. What kind of secrets would she be keeping from him? It's blatantly obvious that Zelda and Link have a thing going in this game. However, the blatantly obvious has never stopped anti-shippers in the past.
You never know, but the quote made it seem as though their definitely is no romantic feelings towards link from Zelda. It makes it seem as though they know this for sure, perhaps she is in love with somebody else like Groose, HA! I would say link has feelings for her though.