The 27-year-old is expected to leave the Liberty Stadium during January, after falling out of favour with new manager Michael Laudrup.
The Black Cats were thought to be close to securing his signature, but now Rangers boss Harry Redknapp has entered the battle.
QPR have the joint worst attacking record in the Premier League, alongside Aston Villa, having netted just 17 times in 21 games.
‘Arry is believed to be keen to correct this, and is considering a £4m swoop for Graham.
He is said to have grown frustrated with current first-choice striker Djibril Cisse and is unsure as to whether Jamie Mackie can deliver the quantity of goals needed for survival.
Graham has been a bit part player with the Swans this term after an impressive 2011/12 season under Brendan Rodgers.
But, he has recently returned to the South Wales club’s first-team, capping some impressive displays with a late equaliser against Arsenal in the FA Cup, forcing a replay.
This has alerted a number of teams including Newcastle, Reading, and Norwich, as well as Sunderland and QPR.