"I have bent over backwards to keep him - I've tried to make him stay," Kinnear told the Evening Chronicle.
"He wants a new challenge and he wants to speak to Manchester City.
"He's done 11 years here and I think he wants a new challenge.
"I left Shay with owner Mike Ashley, club managing director Derek Llambias and Given's lawyer Michael Kennedy, and the talks went on for a few hours.
"It's out of my hands and I am still waiting for the final outcome.
"I would be heartbroken to see him go because he is one of the best keepers in the world. But Man City keep banging on the door to talk to him."