The 27-year-old has played a bit-part role this season but, after starting and scoring in the win over Fulham at the weekend, he is keen to earn further first-team chances
The 27-year-old made 36 Premier League appearances but has seen his playing time restricted by in-form Spanish forward Michu this term.
But, despite being linked with a January move away from the Liberty Stadium, the former Watford striker claims he is open to staying put.
"The gaffer says he wants to sit down with the players who haven't been playing as much," Graham told reporters.
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The Gateshead-born forward, who started and scored as the Swans beat Fulham on Saturday, went on to express his desire for further first-team opportunities.
"It's been very frustrating. I want to play football, I don't want to sit on the bench," he added. "I don't want to sit around and pick up money, I want to play and contribute to the team.
"It's a club that's moving forward and of course I want to be part of it, but I'm not the only one in that situation.
"I haven't gone in and banged on the gaffer's door shouting why I haven't been playing and stuff like that, I've just got my head down in training, played a few under-21 games to keep me ticking over and when the chance has come I felt as though I took it."