"I have set my heart on playing in the Premiership," he told the Manchester Evening News.
Kilkenny made 31 starts during his time with the Latics, with a further three substitute appearances, and scored 5 goals.
Elsewhere, goalkeeper Colin Doyle is now back at St Andrew's after his loan spell at Championship side Nottingham Forest.
The Republic of Ireland Under 21 international made just three starts for the relegated side with a further one appearance coming from the subs bench.
Alex Bruce, who is on-loan at Sheffield Wednesday, will remain with the Yorkshire side until after the League One play-off's. The Owls, who finished 5th in the table, will play 4th placed Brentford home and away for a place in the play-off final.