Brady discovered Given when in charge of Celtic.
He told the Scottish Sun: "I've followed his career with great interest, it's just a pity Celtic fans did not see him. I heard Celtic were interested in trying to get him to go on loan, but that was something that Shay had to sort out with Roberto Mancini.
"He obviously wants to be first-choice.
"It also helps his situation with Ireland if he's a regular with City.
"He is still in the prime of his career as a keeper and could have another six years if he stays fit."