Thorne, who signed an improved three-and-a-half-year contract with the Baggies in January, enjoyed a successful four-month loan spell with the Rams last season, helping Steve McClaren's men to reach the Sky Bet Championship play-off final at Wembley.
Since returning to The Hawthorns he has spoken of his desire to join Derby on a permanent basis.
But the undisclosed offer for the 21-year-old was turned down - and Albion have made it clear that the player was not for sale.
Technical director Terry Burton said: "George has progressed through the Academy into the first-team squad and we have high hopes for him.
"He underlined his potential while on loan at Derby and we have no intentions of selling him. We have told Derby he is not for sale and that is the end of the matter as far as we're concerned.
"The same goes for all of our players. We are not looking to sell anyone. Our only aim is to strengthen our squad this summer - not weaken it."