The Tigers defender has been one of the season’s surprise performers, turning in a number of impressive displays for Steve Bruce’s newly promoted side.
His consistent showings have caught the eye of Everton chief Roberto Martinez, who is said to be ready to make additions to his squad in the coming weeks in a bid to build on a fine opening half of the campaign.
The Spaniard was a fan of Davies while at Wigan, and even attempted to secure his signature.
Now he is keen to make a fresh swoop, but it is understood that Hull have indicated that the 28-year-old will not be sold.
Davies only moved to the KC Stadium over the summer in a £2.25m deal from Birmingham, and is already being talked of as a potential member of Roy Hodgson’s England squad for the 2014 World Cup.
Even if he sees his efforts for the defender thwarted in before the transfer deadline, Martinez is likely to revive his interest at the end of the season.