Although talks are still in the preliminary stages, the Wales international is unhappy with certain aspects being put forward by the Bluebirds.
Ledley, who is expected to feature in Sunday's table-topping clash with Newcastle, insists he wants to stop at City, but the terms offered need to be bettered.
He told the South Wales Echo: "It's down to the club. If they want me to sign, they've got to put a contract to me.
"I want to remain here and if the contract is right I will sign it. At the moment the contract is not right."