Speaking to GQ magazine, Styles said he "didn't even know" about the speculation.
Styles told the magazine: "We're not dating, no. We're just friends."
When asked if he was bisexual, Styles replied: "Bisexual? Me? I don't think so. I'm pretty sure I'm not."
Grimshaw was recently mocked by Keith Lemon on Celebrity Juice over his friendship with Styles.
Styles added that hearing rumours about his sexuality is part of being a celebrity.
He said: "Some of them are funny. Some of them are ridiculous. Some of them are annoying. I don't want to be one of those people that complains about the rumours.
"I never like it when a celebrity goes on Twitter and says, 'This isn't true!' It is what it is. I tend not to do that.
"The only time it gets really annoying is that if you get into a relationship and you get into a place where you really like someone and then things are being written in the papers that affect them and how they see you. Then it can get annoying."
One Direction will appear on one of five different covers for September's edition of GQ, which goes on sale on August 1.