The midfielder has one year left on his current deal and is eager to extend his stay at Parkhead, while also casting an eye to the club's Champions League qualifier versus Elfsborg
The Welshman is in the final year of his deal and keen to extend his stay with the Scottish Premiership champions.
Despite his determination to discuss a contract with manager Neil Lennon, Ledley also wants to focus on Celtic's Uefa Champions League third round second leg tie with Elfsborg on Wednesday.
"Everything is still on hold at the moment," the former Cardiff City man told The Daily Record. "As I said to the gaffer, I'd like to concentrate on the pitch more than off the pitch.
"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."
Celtic head to Sweden with a 1-0 advantage from the first leg, thanks to a Kris Commons winner at Celtic Park and Ledley is eager to reach the group stages of the competition, after getting to the knockout phase last season.
"We don't want Europa League football. Champions League is our aim," he continued.
"Last season was fantastic with the way we played and dealt with it all.
"It was a fantastic honour and they were the best days of my life."
Lennon's men enjoyed a famous victory over Barcelona in Glasgow in the competition last season before bowing out in the round of 16 to Juventus.