The 27-year-old former Hibs forward has had just the one first team outing this season although he has only just returned to training following three months out with a knee injury.
Goal-shy Hearts have been said to be interested in signing him, but Killen is clear he would prefer a switch to the English Premier League, where he began his career with Manchester City.
"I would be interested in moving away. I just want to play football; all the boys at the club are the same," he told the Daily Record.
"When you're not playing, you're not happy so there comes a time when you need to look forward - whether it's a loan or moving on permanently.
"I would like to go back to the Premiership. I think everybody wants to play there.
"That's the level you need to aspire to but, at the moment, I need to work hard to get back in the Celtic side."
"Everybody knows how tough it is at a club like Celtic. We have the biggest squad in the league and the best players so it's a tall order to get a starting position and nail it down. When we look at the players we have on the bench sometimes it shows how tough it is.
"But things can change so quickly. One week you may not be involved then the next you might be starting. I just need to keep working hard, focusing and taking my chance when it comes."