The Welsh midfielder is currently contracted to the summer of 2014 but he is keen to remain in Glasgow and the club is also looking to secure his services for the long-term.
"There are talks going on. I have one more year after this season and hopefully I can stay," he told the Daily Record.
"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."