Stewart was impressed with the performance of Hibernian midfielder McGinn for Scotland against the Netherlands in the friendly international on Thursday evening.
The former Hibernian midfielder believes that the 23-year-old can eventually replace Scott Brown in the Celtic team.
The 36-year-old has also claimed that McGinn is a blend of a young Brown and Stuart Armstrong.
Armstrong is 25 years of age and also operates as a midfielder, and he has earned four caps for Scotland so far in his career.
“Scott’s game has evolved over the years which is natural,” Stewart wrote in The Scottish Sun. “The older you get the more you change.
“He has been in fantastic form over the past 18 months under Brendan Rodgers. And the way he’s playing right now you have got to think he has another campaign in him.
“But you look at Brown and John McGinn and the similarities are there for everyone to see. Right now John is a blend of a young Brown and Armstrong.
“He’s got the legs and the dynamism of Armstrong, but the dig and tackling ability of Broony. And like Kieran Tierney he is someone that will lead by example in the years to come.”
McGinn is one of the best midfielders in the Scottish Premiership at the moment and is playing well for Hibernian.
Celtic are at the top of the Scottish Premiership table at the moment, while Hibernian are currently third in the standings.