The former Hibs player has been sidelined since suffering a fractured ankle during the home Premier League defeat to Southampton on 21 December .
McGinn's rehabilitation has been going well and he is set to train on grass for the first time this weekend as he steps close to a return to action.
"John McGinn has been running on the AlterG (zero-gravity treadmill) at 85 per cent body weight," said Smith ahead of the reverse fixture against Saints on Saturday.
"He's looking to be running on the grass come the weekend. His return will be looked at day-by-day to see how he continues his rehabilitation."
McGinn's progress offers encouragement that he will be fit for Scotland's Euro 2020 play-off semi-final against Israel at Hampden on 26 March.
The midfielder has netted seven goals in seven internationals since Steve Clarke took over as Scotland manager.