Bruce offered a fee of around £1.75m for the Dundee United defender including additional payments on appearances, but the Scottish Premiership club rejected the proposal, according to the Hull Daily Mail.
"We're interested," Bruce said. "We have made a bid that's been rejected at the moment so we'll see what develops over the next few days with that one."
Despite the rejected offer Bruce expects the club to make additions to the squad within the next week, adding: "I expect us to be a bit more active in the next seven days but we just have to be patient."
Bruce's Hull side drew 1-1 in a pre-season friendly at North Ferriby United on Monday evening.