The Hoops defender's contract is up at the end of the season and all the signs are that he will forego the opportunity to extend his current deal.
He has been linked with a move to Middlesbrough, managed by former Celtic boss Gordon Strachan, who was at Parkhead yesterday to see the Old Firm derby which ended in a 1-1 draw after Lee McCulloch equalised two minutes after Scott McDonald had headed the home side into a 79th-minute lead.
The Celtic boss acknowledged that there will be changes made to his squad but only on his terms.
"I am in the market for quality footballers," said Mowbray.
"The board are fully aware of the situation.
"There are a lot of conversations going on at the moment with various clubs, either to sell players or to buy players.
"I don't know if it was Gary Caldwell's last game in a Celtic jersey. We are all very aware of his contract situation and if there are conversations to be had, we will have them.
"What I do know is that we will be in control of whether Gary stays or goes. He is our player, he is under contract and we will decide what is best for this football club, first and foremost."
Aiden McGeady refused to blame referee Steve Conroy for Celtic's failure to reduce Rangers' seven-point lead at the top of the Clydesdale Bank Premier League.
Conroy, officiating in his first game between the Glasgow giants, chalked off a first-half goal from Marc-Antoine Fortune when it looked like he had fairly won an aerial challenge with Rangers goalkeeper Allan McGregor.
The official was also lenient towards Kyle Lafferty when he only showed the Rangers striker a yellow card for a late challenge on Andreas Hinkel.
"You can't really blame the referee for (Celtic) not winning the game, we had more than enough chances to win it," McGeady said. "We should have had the game wrapped up at half-time.
"We had the majority of chances and possession and on another day it could have been three or four."
The Republic of Ireland international reiterated his long-term aim to play in England before claiming his future would be decided by the club.
He said: "I have spoken about it in the past. Everyone has aspirations to play at the top level but if a team came in for me, it wouldn't be up to me if I wanted to go or not, it would be up to the club because I am still under contract."