Arsenal, Fulham and Celtic have all been linked with the Republic of Ireland international, who has lost his place to England's current No.1 Joe Hart following the youngster's return from a loan spell at Birmingham City.
Although 10 years his junior, Schmeichel knows from first hand experience how it feels to lose your place between the Manchester City sticks.
Schmeichel began the 2007/08 season brightly for the Blues before the emergence of Hart pushed the young Dane onto the sidelines. And Schmeichel, like Given, knew he was too good to sit on the bench.
"I hope for Shay's sake that he leaves, because he is too good to be sitting on someone's bench," Schmeichel told talkSPORT.
"It is horrible. I experienced it a lot during my time at City and there's absolutely nothing you can do.
"Goalkeeper is such a specialised position and managers tend to keep it the same all the way through the season so it's very demoralising and disheartening."