The midfielder spent the second half of the 2013/14 campaign on loan at Derby, helping them to the Sky Bet Championship play-off final.
Chief executive Sam Rush is, however, aware that events at the Baggies may delay a deal, with the Premier League club currently focusing their attention on appointing a new manager.
Rush told the Derby Telegraph: "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.
"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.
"We are delighted he enjoyed himself here during his loan spell and we know how well he did for us.
"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."
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