Leeds have told Sheffield United they will have to pay £4 million if they want to sign Kilgannon.
Blades boss Neil Warnock has been given the green light to strengthen his squad and sees his rearguard as an area of priority.
Warnock is poised to contact former assistant Kevin Blackwell to test the water over a possible deal for Kilgallon, who can play at left-back or in central defence.
He wants to add some pace to his backline and sees Kilgallon as a key signing, with an opening offer of around £2million likely to be sent to Elland Road.
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