Following a superb campaign last season, the Irishman has found himself out of favour with Roberto Mancini this term as the Italian continues to select England's Joe Hart ahead of him.
One goalkeeper linked with a move to Eastlands of late is Coventry and former Blues reserve Keiren Westwood.
Ironically the 26-year-old is also Given's understudy for the Republic of Ireland national team, however Mancini is yet to make a move and does not want to offload the former Newcastle star until adding to his bulging squad.
"We can't take the same risk as last season," the Italian told The Guardian.
"We have seen two or three [possible options] but Shay doesn't decide this situation.
"I have talked about this with Shay and he told me that, if we have a chance to take another goalkeeper [he would like to go]... but finding a goalkeeper like Shay?"