The 21-year-old, who only signed a new five-year contract last season season, has impressed this season with manager Neil Lennon and could put pen to paper in the next four weeks.
Lennon said yesterday that he wants to take his young squad into their middle years together.
The Celtic manager also revealed that contract talks are ongoing with Charlie Mulgrew, Victor Wanyama, Joe Ledley and Gary Hooper and the Twardzik twins have already signed.
Lennon expects news on “getting over the line” with some of these “in the next three or four weeks”.
“They are being rewarded for their performances and that’s the incentive we give our players, said Lennon.
“We did it with [Beram] Kayal and [Emilio] Izaguirre and we want to do it with these players. I thought James had a brilliant season last season and I think he’s an exceptional player. We want to tie him down here.
“In time it will be difficult to stop these younger players from moving on but, while they are here, we want to make them feel wanted and rewarded for what they have done on the pitch. Myself and Peter [Lawwell, chief executive] talked about it at the end of the season. We agree or disagree on a few things, but Peter is very supportive on our thinking and it’s a club policy now going back a few years. We hope they all sign a year extension on the contracts – that’s in the club remit. It’s an investment on the club’s part, but I don’t see it that way. They are happy here and enjoying their football and they are not chasing these big, big deals just yet.”