The England U-21 keeper is out of contract in the summer and Leeds offered the youngster and his agent a new deal on Wednesday, which was rejected.
United's Chief Operating Officer Shaun Harvey said on the official Leeds website: "Leeds United have today been informed by the representative of Scott Carson that he has turned down the club's initial offer of a new contract.
"The club intend to keep the dialogue in place with the players agent and hope that a solution can be found that will be satisfactory to both parties.
"It is apparent that our initial offer has not met the players expectations, however, we are committed to trying to keep the player at the club but we have to be aware of the current economic situation in football as a whole, not just at Leeds, and ensure that any contract offer is sustainable in the long term."