Carney, capped 46 times by the Socceroos, was left behind in Tashkent while Bunyodkor travelled to Australia for an Asian Champions League quarter-final clash with Adelaide United on Wednesday night.
Bunyodkor coach Mirjalol Kasimov told reporters through a translator: "In this moment he is still our player. But if he finds any other options, any other club, he can go there, we will terminate our contract with him.
"I have better players who play better than David Carney," he said of the forward who enjoyed stints in England with Sheffield United, Norwich City and Blackpool and in the Netherlands with FC Twente.
Kasimov said Carney always performed better on the international stage, but his priority should be the club.
"When he comes to his national team ... he always plays there better than in our club... he has a contract with the club, he must show the result there (rather) than the national team."