Thorne spent the second half of the season on loan at the Championship team, and after impressing during his time in the East Midlands, he has found himself the subject of further interest from Steve McClaren's side.
Rush told the Derby Telegraph: "I have spoken to West Brom about George and made it clear that we think highly of him and would like to explore the possibility of bringing him here.
"Obviously, West Brom are in a slightly different position to us. They have not got a head coach and they have some changes that they are undertaking.
"So, I would counsel patience but, at the same time, I would also confirm to fans that we believe very much in George."
The 21-year-old scored twice in 12 games during his time at Derby.