6ft 4ins Barnsley-born Parkin signed for the Tigers at the start of this year and scored against United in a 1-0 win at the KC last season.
He has already scored three goals this season even though the Tigers are at the foot of the Championship and, in all, has scored eight goals in 24 appearances.
But Hull chairman Adam Pearson played down speculation linking Parkin with a move and says it is unlikely that there will be any movement of players at the KC before tomorrow's transfer deadline and denied receiving a bid from United for Parkin.