The 28-year-old joined from Birmingham in the summer and has been a valuable member of the meanest home defence in the Premier League, conceding just three times in eight matches at the KC Stadium.
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“It's the first I've heard of it [Everton's bid],” he told the Hull Daily Mail. “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.”