Celtic chief Peter Lawwell admits contract talks with Gary Caldwell have stalled.
Burnley and Middlesbrough have been linked with the former Newcastle United trainee.
Lawwell said: "I haven't spoken to Gary's agent for a couple of months.
"We had preliminary discussions and that's where it starts and ends.
"I wouldn't say there was no chance (of Gary staying) but we have to sit down and see whether it is right for Tony (Mowbray) and right for the club and the player."