The 19-year-old Barnes has been linked with a possible transfer to Tottenham or West Ham and while County value Barnes at more than £5million, Davies confirmed their asking price has not yet been met.
Davies said: "We have had a bid for Giles Barnes but it is nowhere near our valuation for the player - in fact the bid is miles away. We have also had enquiries about him from one or two other clubs but my preference is that Giles Barnes does not leave us because I feel he has unfinished business here at Derby."
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