The 29-year-old has missed a chunk of the season after suffering an issue in the Champions League clash with Shakhtar Donetsk in Poland. The midfielder has had to sit out the last 11 Celtic games. However, he has taken part in training in Sydney ahead of two friendlies against Sydney FC and Everton, while the club are not back in competitive action December 17 when they travel to Aberdeen.
"Hopefully I will be joining bits of the sessions this week and just progressing the rehab,” he told Celtic TV. “It will be an important five, six days for me as well. I am looking forward to getting back on the grass with the boys."
Until the injury, McGregor had missed 17 games since the start of the 2016/17 campaign.