And city rivals Hearts could be ready to step in.
Killen is settling nicely in Edinburgh, and it's thought a reasonable offer from the Jambos and the promise of European football could divert the New Zealand international's attention away from the English Championship.
Vladimir Romanov is ready to look alot closer to home for signings this summer after a season of dissapointment which saw his side fall out of two European competitions before Christmas.
Domestically the Tynecastle side's Title Challenge failed to materialise, and the Jam Tarts have instead been left fighting with Aberdeen for a UEFA Cup place.
Fans are expecting major surgery on the squad this summer, and it is thought 12 or more players could be shown the door to make way for new arrivals.
Killen has scored 14 goals this season despite damaging his cruciate knee ligament in January.