Judge has been sensational for the Bees this season.
Sky Sports claims that the Owls' offer for the 27-year-old fell well short of the Bees' valuation of the player, who has bagged 10 goals and seven assists already in the Championship this season.
And now Carlos Carvalhal's men may find themselves set for a bidding war as they try to lure the attacking midfielder to Hillsborough. Sky Sports reports that Burnley are interested in the former Blackburn man as Sean Dyche attempts to take the Clarets back to the Premier League at the first attempt.
With Judge in such scintillating form - which is a continuation of his efforts from last season where he managed 13 assists in the league - it is hardly a surprise that some of those chasing promotion are so keen to land him heading into the second-half of the campaign.
His energy and creativity will surely be a huge asset to either Wednesday or Burnley, as they both look to put themselves well into the promotion picture.