Given was brought to the club 18 months ago for around £8 million and had an excellent first season at the club. However, Hart's emergence as first-choice after some stellar performances for Birmingham on loan has left Given frozen out and unsure to proceed.
A source close to Given told the Manchester Evening News: "Shay is confused and torn over what to do. He only joined City 18 months ago and wanted to win things after 10 years at Newcastle.
"But he just wants to play and he doesn't see Roberto Mancini leaving Hart out now, even if he makes a mistake. He'll want to stand by his man.
"Shay is watching the situation with the goalkeepers at Arsenal at Fulham. A loan move might be something he'd consider but he's finding it really difficult to know what to do. The last thing he wants to do is risk his place in the Ireland team."
Manchester City manager Roberto Mancini has already claimed he would be open to letting Given leave, although has also maintained he needs quality players in the squad to play as backup to the first-team.
Robinho and Roque Santa Cruz are others who have the green light to depart Eastlands and Mancini admits he would not stand in their way if they request to leave.
"If Robinho, Shay or Roque want to stay, I'm happy because they are fantastic players, but it is most important the players are happy," Mancini told the Times.