The 27-year-old joined the Swans in the summer of 2011 when Brendan Rodgers paid Watford more than £3million for his signature.
But since Michael Laudrup took charge, Graham has struggled to command a regular place - starting less than half of their league games so far this term.
Graham's situation has not gone unnoticed, and reports on Thursday suggest both Reading and Norwich have approached Swansea about a possible £4million deal.
Graham has scored five goals so far this term hopes to have a meeting with manager Michael Laudrup about his long-term prospects.
In an exclusive interview with Sky Sports News, Graham said: "The gaffer stated in the press recently that he wants to talk to everyone who hasn't been playing as much as the others and that's me - that's in my bracket.
"Hopefully over the next few days or so the gaffer will pull me aside and talk to me and let me know what's going on.
"As a footballer, I want to be playing football. If that's not the case and the meeting with the gaffer doesn't go to plan then I'll have to sit down and see what happens - see what offers are on the table.
"I'm 27, it's a short career and I want to be playing games. This could be my last big move... or it couldn't.
"I'm just trying to get on with it, keep my head down and work hard and we'll see what happens in January."