Amid reported interest from Everton and a series of other Premier League clubs, Newcastle have now started to look elsewhere.
However, it is understood that Bruce, who has made no secret of his desire to strengthen his defensive resources, has shown his hand and is attempting to persuade the York-born player.
Kilgallon is valued at around £1.75million by the Blades, who themselves have hopes of winning promotion to the Premier League this season - a factor cited by agent Paul Masterton when he revealed the defender's decision to stay with United.
He said: "We have spoken to [Blades boss] Kevin Blackwell to say Matthew is fully committed to Sheffield United until the end of the season. We have also informed Newcastle United about the situation.
"Matthew is keen to win promotion with Sheffield United. If that happens, we will re-assess the options in the summer.
"It's not about money. It is about picking the right club for a player who wants to play at the highest level during the best years of his career.
"He is totally committed to Sheffield United, has a good rapport with the supporters, and does not want any uncertainty over his future affecting his team-mates."
Bruce also has an interest in Wigan full-back Maynor Figueroa and Hamburg's Guy Demel.
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