Both of the Championship sides are believed to have made £200,00 bids for the 23-year-old centre-back but City Chairman Steve Lansdown has told them both that the player is not for sale.
"We see his future as being with us and that is why we have turned down the offers," he told the clubs official website.
"Unless a club comes in with the sort of money we cannot afford to turn down - as in the case of Leroy Lita - Danny won't be going anywhere."