The 25-year old had his advisors turn down an improved offer for him recently and Sheffield boss Kevin Blackwell is keen to resolve the situation sooner rather than later sop things do not get out of hand.
"We've pushed the boat out and if it goes out any further all the other players would want to jump on it and there'll be no club left," Blackwell said.
"I would have to say that it (a new deal) would appear to be way off. It's a shame. The lad's earning a good living to be honest and it should not be all about money.
"It's affecting him there's no doubt about it and as a manager I want it resolved."
Blackwell added that Kilgallon's agent was having a fair say in what his client was holding out for.
"Agents sow seeds in the players' minds and that affects them and for me that stinks," he added.
"I don't think it's right that his agent comes to the club and holds a gun against our heads and says if you don't go to a certain level we're not prepared to negotiate.
"So it's a frustrating situation. I've got the highest regard for Matthew and I want to get him back to how he was playing last season and hopefully this can be resolved."