Blades assistant manager Stuart McCall says the Blades are planning a transfer window bid for Kilgallon.
"When he played against us last season he was excellent, and I saw him two or three other times and he was their leading player " said McCall.
"So it's a possibility, but at the moment no more than that. We've been linked with a number of players, but Kilgallon keeps coming back and he is a player we have been interested in."
Meanwhile, Luton boss Mike Newell has told any clubs interested in Morgan must meet his own valuation.
Newell says in the Yorkshire Evening Post: "If a club meets your price of a player then I've always maintained that I would never stand in the way of a player.
"It's difficult. You have to have a valuation of players in your mind, and while we don't want to sell people or lose our better players, you still have to have a sensible valuation.
"There has been interest, but as yet nobody has come anywhere near our valuation."