The 26-year-old has just one year remaining on his current deal, but contract talks have stalled in the last couple of weeks.
"Everything is still on hold at the moment. As I said to the gaffer, I'd like to concentrate on the pitch more than off the pitch," Ledley told the Daily Record. "Hopefully, my agent can come up soon to sort everything out and the club offer me a new deal.
"It's a very important couple of weeks. It's a fantastic situation we're in. Hopefully, I can just concentrate on my football first, qualify for the Champions League then go from there.
"I'm getting older. I'm going to be 27 this season. I'm very happy here and it's a fantastic club. This contract is important to me and hopefully it's sorted sooner rather than later."
Ledley joined Celtic from Cardiff City in 2010.