The United chief made headway late last week when star striker Luciano Becchio ended speculation over his own future by agreeing a new three-and-a-half year deal.
Attention is now expected to turn to resolving Kilkenny's future, with the ball-playing midfielder - who can talk to interested parties in January if no new deal is agreed - having no shortage of admirers.
The player, who turned 25 on Sunday, said: "I really want to stay here and feel honoured to play for the club.
"I want to let that be known. I've enjoyed my time here and feel that I've played regularly over the past three years.
"I've made nearly 150 appearances for the club now and that's really a very good record over three seasons.
"Hopefully, the club can sort something out."