Ledley is into the final year of his current contract and there has been no movement on a new deal as yet.
The Wales international is happy to stay at Celtic and says his full focus is on this week's UEFA Champions League qualifier with Elfsborg rather than his own future.
"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," he 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 was exactly the same at Cardiff and I dealt with it well. Hopefully, we can sort something out in the next couple of weeks. I've not properly had a chat with the manager about it but he knows.
"He doesn't want to say too much with one of the most important games coming up in our careers. We're professionals and know how to handle it.
"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."