Celtic chief executive Peter Lawwell believes Gary Caldwell may still have a future at Parkhead.
The defender's contract expires at the end of the season and preliminary discussions have opened about a new deal.
But the defender then upset some fans by voicing his disgruntlement over the contract talks on the day of the Europa League game against Hapoel Tel Aviv in Israel last month.
At Celtic's AGM on Friday, one unhappy shareholder claimed that Caldwell should have been sent home from Israel for voicing his opinions.
Afterwards Lawwell, while admitting talks have not progressed recently, refused to rule out that Caldwell may stay.
He 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."
The issue of money dominated the mostly good-natured AGM, with Lawwell and chairman John Reid rejecting accusations that failure to bolster the squad sufficiently in January had cost the club the SPL title.
While assuring manager Mowbray that money will be available for him to strengthen the side in January, Lawwell admitted that the Hoops could again face frustrations in trying to recruit fresh blood to Parkhead.
He said: "There is finance available and that is not a 'Celtic will break the bank' type of quote.
"We will do all the right things that we did previously and other than last January, we have a decent track record of strengthening at an important time of the season.
"But there are no guarantees because there are so many variables other than finance."