In recent months talks between the club and the midfielder's representatives had previously stalled.
Celtic boss Brendan Rodgers even said that the 25-year old's performances were affected by the uncertainty surrounding his future.
However, it is believed that a new long-term deal could be signed before Saturday's clash with Kilmarnock after talks have been ongoing in the past 24 hours.
The Scotland international, formerly of Dundee United, has been linked with a move to numerous Premier League clubs with his current deal running until 2018.
He has played more than 250 times for Celtic, winning three Scottish Premiership titles, as well as the League Cup and Scottish Cup last season during his time there.