They put a bid of £500k in for the England full-back but Leeds want at least £1.5m to conclude a deal.
The 26-year-old joined the Teessiders on a year's loan in the summer and has indicated he would be keen to stay.
Danny Mills' agent Neil Featherby squashed claims that Mills was holding Boro to ransom over a permanent move.
Boro chairman Steve Gibson and chief executive Keith Lamb are currently trying to sort out a deal with Mills but rumours on Teesside have claimed that the player has made unrealistic demands.
Mills' agent Neil Featherby said: "With regard to Danny's so-called inflated demands in danger of scuppering a permanent move to Middlesbrough, this is absolute rubbish and a long way from the truth.
"Whether it be Middlesbrough, or any other club for that matter, who have made inquiries, they are well aware as to the details of his present contract with Leeds.
"For anyone to suggest he is now looking to hold anyone to ransom by asking for monies which far exceed these current personal terms is total fabrication."