The Voice UK coach was previously reported to be dating the finalist from the show, but the rumours were swiftly denied by his representative at the time.
"No, not at all," O'Donoghue told Capital Breakfast this week when asked directly if he is dating Bruce.
"The story kind of came out of nowhere. We were on TV, we had this moment where we were face-to-face - part of the BBC choreography is you listen to the choreographer and do what they're saying."
He added: "It was one of those moments on TV that everyone was like, 'Oooh, saucy! There's something going on there'. But there's nothing behind it."
When presenter Dave Berry quipped that the choreographer was his 'wing man', O'Donoghue joked: "Yeah yeah yeah, he's me best mate!
"[He said,] 'This is the part when you're going to put your hand on somewhere, and then you're going to go for...' No, not at all."
Rumours of a fling were fuelled last month when O'Donoghue reportedly split from his then-girlfriend Irma Mali, but the Script singer allegedly told friends that the reports were "complete nonsense".
