His agent revealed last week that the former Leeds United stopper was committed to the Blades until the end of the season and that suitors Newcastle United had been informed of the situation.
However, it Sky Sports understand that Burnley made an offer of £1.75million for the 25-year-old, which was accepted by the Blades.
Kilgallon was given permission to hold talks over a move to Turf Moor on Tuesday night, but he has opted to reject Burnley's bid.
He has now gone back to Bramall Lane, where Blades boss Kevin Blackwell has previously stated he would look to reinvest any funds generated from Kilgallon's January departure.
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