A move for the 24-year-old earlier this summer failed but last night Hearts assistant boss Steve Frail said: "We are very hopeful of completing a deal.
"It will be a boost to the squad and will give us competition for places. Stephen can play wide right or in the midfield holding role.
"His biggest asset is his energy as he can go box to box and Neil McCann told me his fitness levels were great when he was at Ibrox.
"We are waiting for the results of his medical, so things are at a reasonably advanced stage."