The Republic of Ireland goalkeeper admits he has always been a fan of the Scottish club and wants first team football after losing his spot at Eastlands to Joe Hart
The Blues' keeper has spent most of this term watching from the sidelines as team-mate Joe Hart's career has rocketed after his return from loan at Birmingham.
Celtic look to be the favourites to sign the Republic of Ireland keeper and the move would see Given following in the footsteps of international team-mate Robbie Keane, who had a successful loan spell at Celtic Park last year.
“Ideally, I would like to be playing but it’s out of my hands," said the ex-Newcastle man to The Daily Star. "If Manchester City want me, I’ve got another two years left on my contract. I don’t really know what’s going to happen."
He went on to say: “It’s no secret I’m a big Celtic supporter and have been all my life.
"It’s a great club, with an unbelievable history, so I wouldn’t look at it as a step down but it’s too soon to say what’s going to happen or if that’s going to happen. I don't know what the current goalkeeping situation is.
“Fraser Forster had a very good season up there and there has been talk of him moving on a permanent basis so we would have to wait and see. But it is a fantastic club with fantastic supporters.
"You never say never when Celtic come calling.”