The 25-year-old has been training with the Championship side this week, in the hope of securing a deal.
McClaren has admitted that he has been impressed with Dawkins.
"I know Simon very well. I very nearly took him to Holland with me when I was at FC Twente and he was at Queens Park Rangers for a couple of weeks when I was there. I know what he can do," McClaren told the Derby Telegraph.
"He has come in and adjusted and there might be a possibility of doing something with him. We are looking at that."