The Wales international still has 18 months left to run on a deal agreed on his arrival at Parkhead in July 2010.
Ledley is, however, open to the idea of putting fresh terms in place. The 25-year-old is loving life in Scotland and believes he could not be at a better club at this stage of his career.
Fresh from helping Celtic to a famous 2-1 victory over Barcelona in the UEFA Champions League on Wednesday, Ledley told the Daily Record: "There are talks going on. I have one more year after this season and hopefully I can stay.
"It's a fantastic club, I love playing for Celtic.
"Talks have started and I have spoken to my agent so hopefully something can happen.
"People are always going to criticise Scottish football for some reason. I think it's a fantastic league. To play in the Champions League is a huge honour too. It was a great move for me to sign for Celtic."
Ledley is aware that some may have questioned his ambition when he left Cardiff City for Celtic as a free agent two years ago, but he hopes the success he has enjoyed in Glasgow has helped to silence those critics.
He added: "I could have maybe gone to a Premier League team and just sat in mid-table. I didn't want that.
"I like winning games, I want to win things and play in the best competition in the world, the Champions League."