City boss Roberto Mancini has told Given he would be free to leave the club in January if he wants a move.
But the club are ready to go over the head of the Italian manager by offering Given a new contract, according to News of the World.
Given is frustrated by the lack of regular first-team football at Eastlands, but City are keen to keep the keeper at the club as back up for Joe Hart.
City are reportedly ready to improve Given’s current £90,000-a-week deal.
