The centre-back has made a big impact since arriving at the KC Stadium from Championship side Birmingham City in June.
Hull boast the best home defensive record in the Premier League having conceded only three goals in eight games.
Davies has caught the eye with some consistently impressive performances and Everton boss Roberto Martinez has reportedly taken note.
The Spaniard has been linked with a £6 million bid for the former West Brom man, but Hull manager Bruce has no plans to let one of his key players leave unless the club receive an offer they are unable to refuse.
He told the Hull Daily Mail: "It's the first I've heard of it,
"There's going to be speculation about any player that's doing well and Curtis is doing well.
"I don't even have to bother with my owner with £6m. We don't want to lose our good players and that wouldn't even tempt us.
"I wouldn't even have to ask the question on it and that's the strength we've got.
"We all realise how important Curtis has been to us and for anyone to sell their best players now it would have to be at a premium which would blow us away,
"That wouldn't even scratch the surface. Where could I replace Curtis Davies in January for that amount? The last thing I want to do is dismantle a squad I'm trying to put together.
"I'm not naive enough to think every player hasn't got a price but not at that sort of money."
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