The 21-year-old midfielder spent the latter half of last season on loan at the iPro Stadium, helping Steve McClaren's side reach the Championship play-off final.
It was Thorne's fourth loan spell away from The Hawthorns and he is yet to establish himself in the first team since coming through their youth system after joining from Cambridge United.
With his future at the club unclear, Derby's chief executive Sam Rush has confirmed the club's desire to sign Thorne permanently following his 12 appearances last term.
"I have spoken to West Brom about George and made it clear we think highly of him and would like to explore the possibility of bringing him here," Rush told The Derby Telegraph .
"Obviously, West Brom are in a slightly different position to us. They have not got a head coach and they have some changes they are undertaking.
"So, I would counsel patience but, at the same time, I would also confirm to fans we believe very much in George.
"Steve McClaren is a big admirer of George, so we will do our best to bring him to the club during the course of the summer."
West Brom are currently without a coach, having parted company with Pepe Mel earlier in May.
