The former Scotland international, 29, has been training with Grayson's squad for the last two weeks.
Grayson said: "He's done OK while he's been here and shown the qualities that have seen him play for the likes of Manchester United and Hearts.
"Because he's done well and fitted in well, we're going to take more of a look at him and see how things go."
Stewart, who has won four caps for Scotland, began his career at Old Trafford and has had spells with Nottingham Forest, Hibernian and Hearts.
Source: PA
