The reports suggest Rangers manager Chris Ramsey wants a commanding centre-back and has earmarked the 30-year-old as someone who can aid their promotion push following the loan of Steven Caulker to Southampton.
While the Hull defender is seen as the Loftus Road outfit's first-choice, the club are also said to be pondering a move for West Ham's James Collins, who, according to London24, is free to leave the Upton Park this summer.
Davies made 21 appearances for the Tigers last season, averaging an outstanding 14 defensive actions per match - including a total 217 clearances, 67 clearances and 18 blocks.
Thus far he has featured on four occasions in Hull's Championship campaign, impressing greatly as the club have moved quickly to assume a position in the play-off spots.
He started for the club against Charlton on Saturday but was in and out of the side last season and Steve Bruce may be have a big decision to make if QPR come in with a high offer.