Blues boss Alex McLeish has revealed that Blues approached City in an attempt to sign Hart, who is on a season loang loan deal at St Andrews, but City have said that the England international keeper is not for sale.
"City will take Joe Hart back at the end of the season," McLeish told The Guardian.
"There is no chance of us signing him in January. We asked the question and they said that won't happen. We never had an option from City to buy him.
"He has the comfort of knowing City really want him and he is part of their future."
However, McLeish is not giving up hope of being able to re-sign Hart on loan again in the summer.
"Joe Hart remains a big part of the future. But you couldn't rule out that Joe stays with us in the summer.
"They said he was going out for experience to improve and he has improved.
"It doesn't preclude him from coming back and we can negotiate with City for another year."