Coles has a year left on his Ashton Gate contract but appears reluctant to sign an extention. He wants Champoionship football with both Cardiff and Hull in the chase.
"We can't afford to lose him and I hope we can fight as much as possible to keep him," Bristol City boss Brian Tinnion told BBC Radio Bristol.
"He wants to play in the Championship but I want him to stay and get us there and we're negotiating a new contract."
23 year old Coles has played nearly 150 league games.
"We see his future as being with us and that is why we have turned down the offers," Chairman Steve Lansdown told the club's 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."