The 27-year-old scored 14 goals for the Swans last term but has been restricted to a bit-part role this time around, starting just nine games and netting only three goals.
His chances have been limited by the outstanding form of Spanish forward Michu, and although he has many admirers in both the Premier League and Championship, Graham is willing to stay and fight for his place.
"I don't see a reason to leave," he said. "I don't know where these rumours come from. I can't say enough times on Twitter about them.
"It was Wolves yesterday apparently, then there was Cardiff, Norwich, Sunderland, Reading, Aston Villa - I have been linked with everyone.
"But the gaffer hasn't said he doesn't want me here so I don't see a reason to be looking elsewhere.
"Don't get me wrong, I don't like sitting on the bench and just picking up money, I want to be playing.
"But the gaffer hasn't said he doesn't want me and that is probably the only time I will go - if the gaffer says we have accepted a bid."
Graham signed for Swansea for £3.5m from Watford in June 2011 and impressed during the club's first season back in the top flight under Brendan Rodgers.
Losing his place this in the starting line-up this year has consequently been a bitter pill to swallow.
He added: "It is a difficult moment for me, but the team are doing well, which is the most important thing.
"If I get a chance to come on or start a game I will be looking to score a goal and kick-start my season.
"It has been a frustrating couple of months for me and it would be nice to get that goal, but as long as the team are doing well it doesn't really matter."
Graham is adamant his time out of the starting line-up has not affected his morale.
"My confidence isn't low," he said. "I would obviously like to get a little run in the team, to get my match fitness up and to get a bit sharper, but I have been working hard off the pitch to stay in shape for when I'm called upon."