The Currie youngster impressed the Glasgow coach after he replaced the injured Sam Pinder on Monday.
Today's Daily Record reports that Sam is likely to miss Saturday's challenge match at Hughenden after he was taken off with a damaged knee in the opening minutes of the training game against Ayr at Millbrae.
With Glasgow's other scrum-half Graeme Beveridge still undergoing rehab in the wake of cartilage surgery, Graham looks set to appear from the start.
Hugh said: "Graham fitted in really well, considering he had only linked up with the rest of the squad an hour or so before kick-off. Despite Sam's injury we gained a lot from the exercise against Ayr.
"But Rotherham (Earth Titans) will be a couple of steps up and there is no doubt we'll have to raise our game accordingly."