After the defender was linked with Wigan and Birmingham there have been reports that the negotiations have stalled.
Blackwell has played down any worries over Kilgallon's future at the club and plans a fresh round before the new season gets underway.
"Everything is still ongoing," Blackwell told the Sheffield Star. "In any case, Killa is still under contract with us for another year. We've taken up options on everyone who had one.
"So there's no crisis. We'll be having another chat with him before the start of the season."