The 21-year-old striker has returned from a productive loan spell at Notts County to join the Hoops squad on tour in Austria.
McGregor netted 14 goals for the League One side last term and is determined to catch the eye of boss Ronny Deila.
He said: "The new manager has come in and brought some really good ideas in terms of how he wants to play.
"So it's a fresh start for everyone, especially the young boys because if you impress, who knows where you can go?
"I just want to take the confidence and my experience of last season into these 12 days and try and impress as much as I can in the training and the games, and see where that takes me."