"There will be no romance between the Straw Hats in One Piece"- In an SBS question, Oda was asked about romance between the straw hats. He ended up jokingly dodging the question, not actually saying no. People can assume that there will be no romance based on how Oda tends to be with his views on his series's demographic, but he's never stated one way or the other.

Actually he did say he *doesn't think* there'll be any romance among the crew. It isn't well-known, but in a response to a question asking about who Nami likes, Oda said:

Hmm, in a romantic sense? I don't think there will be any romance among the crew. Nami probably sees all the good aspects/qualities of those guys, but One Piece isn't a romance. Maybe a lot of girl readers ask this kind of question. Boys are not interested at all. One Piece is basically a shonen manga, manga for boys, so romance isn't depicted.

I have no idea why I can't find this specific quote online though and I'm unsure of when he said it (I heard someone mention it was from Jump Festa 2008 but I unable to confirm). However, this response can be found in that special small booklet of the first pilot OP chapter, Romance Dawn, that comes with the 1st box set of the OP manga. Here's a picture for reference.