The 26-year-old, who departed Hearts at the end of last season, has been on trial with the Championship club in recent weeks.
"We're taking a look at Danny right now and he's already featured in a couple of our pre-season games," Rae told Sky Sports News.
"We want to take a look at him although a deal isn't imminent. I know Danny well from his time at Hearts and although he's had a few injuries he's a good player.
"So we will take another look at him this weekend and all being well there might be a deal on the table for him."
Grainger spent a week training with Sheffield United earlier in the summer, but a move failed to materialise.