Comments attributed to Coyne in the Australian media suggest he is considering a move away from the club with an agreement for him to leave already in place.
Colchester chief executive Steve Bradshaw insists no such agreement is in place but admits the club will have to hold talks with the defender to resolve his future.
"As with all of our players, there was a meeting with the manager at the end of the season and Chris probably hasn't played as many games as he would have liked over the past year," he told the club's official website.
"However, there is no agreement in place to let him cancel his contract with the club.
"It seems at this moment in time he has concerns over his future and how regularly he is playing. Therefore all parties involved will be having further discussions to clarify Chris' situation."