Given, 34, has been told by coach Roberto Mancini that a decision has not yet been made on who will start this weekend's Premier League opener away to Tottenham Hotspur. But if Hart, likely to start England's friendly with Hungary on Wednesday, get the nod then Given will have to consider his future.
The goalkeeper has admitted he would be willing to leave the club on loan if he is not first choice.
"We will have to wait until lunchtime on Saturday when the manager picks the team to see who starts in goal,'' said Given, who has been linked with Arsenal and Fulham. "Obviously I hope to start, but it's inevitable there is going to be speculation because I know Joe is also a top 'keeper.
"The manager will decide, and whoever he starts with you would feel that is who he would mostly want to play in the big games. If I don't start then I'll sit down with the club next week and see where my future lies, and maybe vice-versa with Joe, because we will both feel we should be playing.
"Ideally I'd like to stay at the club because it's a big club to be at, a very ambitious club with fantastic owners. I want to be part of it, which is why I joined in the first place. If I don't start I guess it's an advantage the transfer window will still be open.
"Maybe I'll go out on loan, come back and see where that takes me. But I know I'm at a stage where I need to be playing. I'm 34, and I've not got millions of years left.''
Given fully believes Hart will start for England in their friendly against Hungary at Wembley on Wednesday. That in turn would lead to its own pressures as England manager Fabio Capello would want Hart to be a first-team regular with City.
"There's so much stuff in England at the moment regarding Joe and the England goalkeeping situation,'' added Given. "I don't know if that would influence the manager, you would need to ask him, but I do understand. I'm sure Joe will play on Wednesday, so the situation is an interesting one.''
Asked whether he feels Hart will become England number one, Given replied: "Only if he's playing, which is the same for me because I need to be playing every week to be with the Ireland team.''