The 53-year-old was reportedly a candidate to take over from Mauricio Pochettino at St Mary's Stadium following the Argentine's move to Tottenham Hotspur.
However, Bruce insists that it was never in his thoughts to leave Hull ahead of the new Premier League campaign.
"I don't know where that came from," he told the Hull Daily Mail. "I haven't got an agent but all agents seem to claim to represent me. That means a lot of rubbish comes out.
"There was never any intention for me to move on. I've said it from day one that I'm perfectly happy here."
Hull start the new Premier League season on Saturday when they play Queens Park Rangers at Loftus Road.